


import unittest

from transformers import LayoutLMConfig, is_torch_available
from transformers.testing_utils import require_torch, slow, torch_device

from ...test_configuration_common import ConfigTester
from ...test_modeling_common import ModelTesterMixin, ids_tensor
from ...test_pipeline_mixin import PipelineTesterMixin


if is_torch_available():
					import torch

					from transformers import (
					    LayoutLMForMaskedLM,
					    LayoutLMForQuestionAnswering,
					    LayoutLMForSequenceClassification,
					    LayoutLMForTokenClassification,
					    LayoutLMModel,
					)

class      __snake_case				:
					def __init__(						self       :						Any	,      _lowerCAmelCase       :						List[str]	,      _lowerCAmelCase       :						Optional[int]=1_3	,      _lowerCAmelCase       :						Union[str, Any]=7	,      _lowerCAmelCase       :						Union[str, Any]=True	,      _lowerCAmelCase       :						Optional[int]=True	,      _lowerCAmelCase       :						Union[str, Any]=True	,      _lowerCAmelCase       :						Union[str, Any]=True	,      _lowerCAmelCase       :						Optional[Any]=9_9	,      _lowerCAmelCase       :						Optional[int]=3_2	,      _lowerCAmelCase       :						int=5	,      _lowerCAmelCase       :						Union[str, Any]=4	,      _lowerCAmelCase       :						Tuple=3_7	,      _lowerCAmelCase       :						Optional[Any]="gelu"	,      _lowerCAmelCase       :						Dict=0.1	,      _lowerCAmelCase       :						str=0.1	,      _lowerCAmelCase       :						Dict=5_1_2	,      _lowerCAmelCase       :						Union[str, Any]=1_6	,      _lowerCAmelCase       :						List[str]=2	,      _lowerCAmelCase       :						int=0.02	,      _lowerCAmelCase       :						Optional[Any]=3	,      _lowerCAmelCase       :						Dict=4	,      _lowerCAmelCase       :						List[Any]=None	,      _lowerCAmelCase       :						int=1_0_0_0	,      )							->					Optional[Any]:



											'''simple docstring'''





											__magic_name__					=      parent
											__magic_name__					=      batch_size
											__magic_name__					=      seq_length
											__magic_name__					=      is_training
											__magic_name__					=      use_input_mask
											__magic_name__					=      use_token_type_ids
											__magic_name__					=      use_labels
											__magic_name__					=      vocab_size
											__magic_name__					=      hidden_size
											__magic_name__					=      num_hidden_layers
											__magic_name__					=      num_attention_heads
											__magic_name__					=      intermediate_size
											__magic_name__					=      hidden_act
											__magic_name__					=      hidden_dropout_prob
											__magic_name__					=      attention_probs_dropout_prob
											__magic_name__					=      max_position_embeddings
											__magic_name__					=      type_vocab_size
											__magic_name__					=      type_sequence_label_size
											__magic_name__					=      initializer_range
											__magic_name__					=      num_labels
											__magic_name__					=      num_choices
											__magic_name__					=      scope
											__magic_name__					=      range_bbox
					def 	a			(						self       :						int  )							->					str:



											'''simple docstring'''





											__magic_name__					=      ids_tensor([self.batch_size, self.seq_length]	,      self.vocab_size  )

											__magic_name__					=      ids_tensor([self.batch_size, self.seq_length, 4]	,      self.range_bbox  )
											# Ensure that bbox is legal
											for i in range(bbox.shape[0]  ):
																	for j in range(bbox.shape[1]  ):
																							if bbox[i, j, 3] < bbox[i, j, 1]:
																													__magic_name__					=      bbox[i, j, 3]
																													__magic_name__					=      bbox[i, j, 1]
																													__magic_name__					=      t
																							if bbox[i, j, 2] < bbox[i, j, 0]:
																													__magic_name__					=      bbox[i, j, 2]
																													__magic_name__					=      bbox[i, j, 0]
																													__magic_name__					=      t

											__magic_name__					=      None
											if self.use_input_mask:
																	__magic_name__					=      ids_tensor([self.batch_size, self.seq_length]	,      vocab_size=2  )

											__magic_name__					=      None
											if self.use_token_type_ids:
																	__magic_name__					=      ids_tensor([self.batch_size, self.seq_length]	,      self.type_vocab_size  )

											__magic_name__					=      None
											__magic_name__					=      None
											__magic_name__					=      None
											if self.use_labels:
																	__magic_name__					=      ids_tensor([self.batch_size]	,      self.type_sequence_label_size  )
																	__magic_name__					=      ids_tensor([self.batch_size, self.seq_length]	,      self.num_labels  )
																	__magic_name__					=      ids_tensor([self.batch_size]	,      self.num_choices  )

											__magic_name__					=      self.get_config()

											return config, input_ids, bbox, token_type_ids, input_mask, sequence_labels, token_labels, choice_labels
					def 	a			(						self       :						Any  )							->					List[Any]:



											'''simple docstring'''





											return LayoutLMConfig(
											    vocab_size=self.vocab_size	,      hidden_size=self.hidden_size	,      num_hidden_layers=self.num_hidden_layers	,      num_attention_heads=self.num_attention_heads	,      intermediate_size=self.intermediate_size	,      hidden_act=self.hidden_act	,      hidden_dropout_prob=self.hidden_dropout_prob	,      attention_probs_dropout_prob=self.attention_probs_dropout_prob	,      max_position_embeddings=self.max_position_embeddings	,      type_vocab_size=self.type_vocab_size	,      initializer_range=self.initializer_range	,      )
					def 	a			(						self       :						Tuple	,      _lowerCAmelCase       :						Dict	,      _lowerCAmelCase       :						str	,      _lowerCAmelCase       :						Union[str, Any]	,      _lowerCAmelCase       :						str	,      _lowerCAmelCase       :						Tuple	,      _lowerCAmelCase       :						Any	,      _lowerCAmelCase       :						Dict	,      _lowerCAmelCase       :						Union[str, Any]  )							->					str:



											'''simple docstring'''





											__magic_name__					=      LayoutLMModel(config=__lowerCAmelCase  )
											model.to(__lowerCAmelCase  )
											model.eval()
											__magic_name__					=      model(__lowerCAmelCase	,      __lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase  )
											__magic_name__					=      model(__lowerCAmelCase	,      __lowerCAmelCase	,      token_type_ids=__lowerCAmelCase  )
											__magic_name__					=      model(__lowerCAmelCase	,      __lowerCAmelCase  )
											self.parent.assertEqual(result.last_hidden_state.shape	,      (self.batch_size, self.seq_length, self.hidden_size)  )
											self.parent.assertEqual(result.pooler_output.shape	,      (self.batch_size, self.hidden_size)  )
					def 	a			(						self       :						Tuple	,      _lowerCAmelCase       :						str	,      _lowerCAmelCase       :						Dict	,      _lowerCAmelCase       :						Any	,      _lowerCAmelCase       :						Any	,      _lowerCAmelCase       :						Union[str, Any]	,      _lowerCAmelCase       :						int	,      _lowerCAmelCase       :						Optional[Any]	,      _lowerCAmelCase       :						Optional[Any]  )							->					List[Any]:



											'''simple docstring'''





											__magic_name__					=      LayoutLMForMaskedLM(config=__lowerCAmelCase  )
											model.to(__lowerCAmelCase  )
											model.eval()
											__magic_name__					=      model(__lowerCAmelCase	,      __lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase	,      labels=__lowerCAmelCase  )
											self.parent.assertEqual(result.logits.shape	,      (self.batch_size, self.seq_length, self.vocab_size)  )
					def 	a			(						self       :						str	,      _lowerCAmelCase       :						Optional[Any]	,      _lowerCAmelCase       :						Dict	,      _lowerCAmelCase       :						Tuple	,      _lowerCAmelCase       :						Optional[int]	,      _lowerCAmelCase       :						Optional[int]	,      _lowerCAmelCase       :						Tuple	,      _lowerCAmelCase       :						Optional[int]	,      _lowerCAmelCase       :						str  )							->					str:



											'''simple docstring'''





											__magic_name__					=      self.num_labels
											__magic_name__					=      LayoutLMForSequenceClassification(__lowerCAmelCase  )
											model.to(__lowerCAmelCase  )
											model.eval()
											__magic_name__					=      model(
											    __lowerCAmelCase	,      __lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase	,      labels=__lowerCAmelCase  )
											self.parent.assertEqual(result.logits.shape	,      (self.batch_size, self.num_labels)  )
					def 	a			(						self       :						Optional[Any]	,      _lowerCAmelCase       :						Tuple	,      _lowerCAmelCase       :						Any	,      _lowerCAmelCase       :						int	,      _lowerCAmelCase       :						Tuple	,      _lowerCAmelCase       :						List[str]	,      _lowerCAmelCase       :						Dict	,      _lowerCAmelCase       :						Tuple	,      _lowerCAmelCase       :						Optional[int]  )							->					Optional[int]:



											'''simple docstring'''





											__magic_name__					=      self.num_labels
											__magic_name__					=      LayoutLMForTokenClassification(config=__lowerCAmelCase  )
											model.to(__lowerCAmelCase  )
											model.eval()
											__magic_name__					=      model(__lowerCAmelCase	,      __lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase	,      labels=__lowerCAmelCase  )
											self.parent.assertEqual(result.logits.shape	,      (self.batch_size, self.seq_length, self.num_labels)  )
					def 	a			(						self       :						Tuple	,      _lowerCAmelCase       :						Dict	,      _lowerCAmelCase       :						Optional[Any]	,      _lowerCAmelCase       :						List[Any]	,      _lowerCAmelCase       :						Any	,      _lowerCAmelCase       :						Union[str, Any]	,      _lowerCAmelCase       :						List[Any]	,      _lowerCAmelCase       :						int	,      _lowerCAmelCase       :						Optional[int]  )							->					Any:



											'''simple docstring'''





											__magic_name__					=      LayoutLMForQuestionAnswering(config=__lowerCAmelCase  )
											model.to(__lowerCAmelCase  )
											model.eval()
											__magic_name__					=      model(
											    __lowerCAmelCase	,      bbox=__lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase	,      start_positions=__lowerCAmelCase	,      end_positions=__lowerCAmelCase	,      )
											self.parent.assertEqual(result.start_logits.shape	,      (self.batch_size, self.seq_length)  )
											self.parent.assertEqual(result.end_logits.shape	,      (self.batch_size, self.seq_length)  )







					def 	a			(						self       :						List[str]  )							->					Tuple:



											'''simple docstring'''





											__magic_name__					=      self.prepare_config_and_inputs()
											(
											    (
											    __magic_name__      
											)		,      (
											    __magic_name__      
											)		,      (
											    __magic_name__      
											)		,      (
											    __magic_name__      
											)		,      (
											    __magic_name__      
											)		,      (
											    __magic_name__      
											)		,      (
											    __magic_name__      
											)		,      (
											    __magic_name__      
											)		,            
											)					=      config_and_inputs
											__magic_name__					=      {
											    'input_ids': input_ids,
											    'bbox': bbox,
											    'token_type_ids': token_type_ids,
											    'attention_mask': input_mask,
											}
											return config, inputs_dict







@require_torch
class      __snake_case				(   _lowercase	,      _lowercase	,      unittest.TestCase):
					SCREAMING_SNAKE_CASE_		:       List[str]								=			(
					    (
					        LayoutLMModel,
					        LayoutLMForMaskedLM,
					        LayoutLMForSequenceClassification,
					        LayoutLMForTokenClassification,
					        LayoutLMForQuestionAnswering,
					    )
					    if is_torch_available()
					    else None
					)
					SCREAMING_SNAKE_CASE_		:       List[str]								=			(
					    {
					        "document-question-answering": LayoutLMForQuestionAnswering,
					        "feature-extraction": LayoutLMModel,
					        "fill-mask": LayoutLMForMaskedLM,
					        "text-classification": LayoutLMForSequenceClassification,
					        "token-classification": LayoutLMForTokenClassification,
					        "zero-shot": LayoutLMForSequenceClassification,
					    }
					    if is_torch_available()
					    else {}
					)
					SCREAMING_SNAKE_CASE_		:       Optional[Any]								=			True
					def 	a			(						self       :						Tuple  )							->					Union[str, Any]:



											'''simple docstring'''





											__magic_name__					=      LayoutLMModelTester(self  )
											__magic_name__					=      ConfigTester(self	,      config_class=__lowerCAmelCase	,      hidden_size=3_7  )
					def 	a			(						self       :						int  )							->					List[Any]:



											'''simple docstring'''





											self.config_tester.run_common_tests()
					def 	a			(						self       :						List[Any]  )							->					Any:



											'''simple docstring'''





											__magic_name__					=      self.model_tester.prepare_config_and_inputs()
											self.model_tester.create_and_check_model(*__lowerCAmelCase  )
					def 	a			(						self       :						Optional[Any]  )							->					Optional[int]:



											'''simple docstring'''





											__magic_name__					=      self.model_tester.prepare_config_and_inputs()
											for type in ["absolute", "relative_key", "relative_key_query"]:
																	__magic_name__					=      type
																	self.model_tester.create_and_check_model(*__lowerCAmelCase  )
					def 	a			(						self       :						Any  )							->					Optional[int]:



											'''simple docstring'''





											__magic_name__					=      self.model_tester.prepare_config_and_inputs()
											self.model_tester.create_and_check_for_masked_lm(*__lowerCAmelCase  )
					def 	a			(						self       :						Any  )							->					Dict:



											'''simple docstring'''





											__magic_name__					=      self.model_tester.prepare_config_and_inputs()
											self.model_tester.create_and_check_for_sequence_classification(*__lowerCAmelCase  )
					def 	a			(						self       :						List[str]  )							->					Optional[Any]:



											'''simple docstring'''





											__magic_name__					=      self.model_tester.prepare_config_and_inputs()
											self.model_tester.create_and_check_for_token_classification(*__lowerCAmelCase  )
					def 	a			(						self       :						Optional[int]  )							->					int:



											'''simple docstring'''





											__magic_name__					=      self.model_tester.prepare_config_and_inputs()
											self.model_tester.create_and_check_for_question_answering(*__lowerCAmelCase  )







					@unittest.skip('Will be fixed soon by reducing the size of the model used for common tests.'  )
					def 	a			(						self       :						Optional[Any]  )							->					Union[str, Any]:



											'''simple docstring'''





											pass







def 				UpperCamelCase_	(					)->   List[str]:




						'''simple docstring'''
						# Here we prepare a batch of 2 sequences to test a LayoutLM forward pass on:
						# fmt: off
						__magic_name__					=      torch.tensor([[1_01,10_19,10_14,10_16,10_37,1_28_49,47_47,10_04,1_42_46,22_78,54_39,45_24,50_02,29_30,21_93,29_30,43_41,32_08,10_05,10_55,21_71,28_48,1_13_00,35_31,1_02],[1_01,40_70,40_34,70_20,10_24,30_58,10_15,10_13,28_61,10_13,60_70,1_92_74,27_72,62_05,2_78_14,1_61_47,1_61_47,43_43,20_47,1_02_83,1_09_69,1_43_89,10_12,23_38,1_02]]						,      device=_lowercase  )  # noqa: E231
						__magic_name__					=      torch.tensor([[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],]						,      device=_lowercase  )  # noqa: E231
						__magic_name__					=      torch.tensor([[[0,0,0,0],[4_23,2_37,4_40,2_51],[4_27,2_72,4_41,2_87],[4_19,1_15,4_37,1_29],[9_61,8_85,9_92,9_12],[2_56,38,3_30,58],[2_56,38,3_30,58],[3_36,42,3_53,57],[3_60,39,4_01,56],[3_60,39,4_01,56],[4_11,39,4_71,59],[4_79,41,5_28,59],[5_33,39,6_30,60],[67,1_13,1_34,1_31],[1_41,1_15,2_09,1_32],[68,1_49,1_33,1_66],[1_41,1_49,1_87,1_64],[1_95,1_48,2_87,1_65],[1_95,1_48,2_87,1_65],[1_95,1_48,2_87,1_65],[2_95,1_48,3_49,1_65],[4_41,1_49,4_92,1_66],[4_97,1_49,5_46,1_64],[64,2_01,1_25,2_18],[10_00,10_00,10_00,10_00]],[[0,0,0,0],[6_62,1_50,7_54,1_66],[6_65,1_99,7_42,2_11],[5_19,2_13,5_54,2_28],[5_19,2_13,5_54,2_28],[1_34,4_33,1_87,4_54],[1_30,4_67,2_04,4_80],[1_30,4_67,2_04,4_80],[1_30,4_67,2_04,4_80],[1_30,4_67,2_04,4_80],[1_30,4_67,2_04,4_80],[3_14,4_69,3_76,4_82],[5_04,6_84,5_82,7_06],[9_41,8_25,9_73,9_00],[9_41,8_25,9_73,9_00],[9_41,8_25,9_73,9_00],[9_41,8_25,9_73,9_00],[6_10,7_49,6_52,7_65],[1_30,6_59,1_68,6_72],[1_76,6_57,2_37,6_72],[2_38,6_57,3_12,6_72],[4_43,6_53,6_28,6_72],[4_43,6_53,6_28,6_72],[7_16,3_01,8_25,3_17],[10_00,10_00,10_00,10_00]]]						,      device=_lowercase  )  # noqa: E231
						__magic_name__					=      torch.tensor([[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]						,      device=_lowercase  )  # noqa: E231
						# these are sequence labels (i.e. at the token level)
						__magic_name__					=      torch.tensor([[-1_00,10,10,10,9,1,-1_00,7,7,-1_00,7,7,4,2,5,2,8,8,-1_00,-1_00,5,0,3,2,-1_00],[-1_00,12,12,12,-1_00,12,10,-1_00,-1_00,-1_00,-1_00,10,12,9,-1_00,-1_00,-1_00,10,10,10,9,12,-1_00,10,-1_00]]						,      device=_lowercase  )  # noqa: E231
						# fmt: on

						return input_ids, attention_mask, bbox, token_type_ids, labels




@require_torch
class      __snake_case				(   unittest.TestCase):
					@slow
					def 	a			(						self       :						int  )							->					List[str]:



											'''simple docstring'''





											__magic_name__					=      LayoutLMModel.from_pretrained('microsoft/layoutlm-base-uncased'  ).to(__lowerCAmelCase  )

											__magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__					=      prepare_layoutlm_batch_inputs()

											# forward pass
											__magic_name__					=      model(input_ids=__lowerCAmelCase	,      bbox=__lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase  )

											# test the sequence output on [0, :3, :3]
											__magic_name__					=      torch.tensor(
											    [[0.1785, -0.1947, -0.0425], [-0.3254, -0.2807, 0.2553], [-0.5391, -0.3322, 0.3364]]	,      device=__lowerCAmelCase	,      )

											self.assertTrue(torch.allclose(outputs.last_hidden_state[0, :3, :3]	,      __lowerCAmelCase	,      atol=1E-3  )  )

											# test the pooled output on [1, :3]
											__magic_name__					=      torch.tensor([-0.6580, -0.0214, 0.8552]	,      device=__lowerCAmelCase  )

											self.assertTrue(torch.allclose(outputs.pooler_output[1, :3]	,      __lowerCAmelCase	,      atol=1E-3  )  )
					@slow
					def 	a			(						self       :						Optional[int]  )							->					Union[str, Any]:



											'''simple docstring'''





											__magic_name__					=      LayoutLMForSequenceClassification.from_pretrained('microsoft/layoutlm-base-uncased'	,      num_labels=2  ).to(
											    __lowerCAmelCase  )

											__magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__					=      prepare_layoutlm_batch_inputs()

											# forward pass
											__magic_name__					=      model(
											    input_ids=__lowerCAmelCase	,      bbox=__lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase	,      labels=torch.tensor([1, 1]	,      device=__lowerCAmelCase  )	,      )

											# test whether we get a loss as a scalar
											__magic_name__					=      outputs.loss
											__magic_name__					=      torch.Size([]  )
											self.assertEqual(loss.shape	,      __lowerCAmelCase  )

											# test the shape of the logits
											__magic_name__					=      outputs.logits
											__magic_name__					=      torch.Size((2, 2)  )
											self.assertEqual(logits.shape	,      __lowerCAmelCase  )
					@slow
					def 	a			(						self       :						Union[str, Any]  )							->					Union[str, Any]:



											'''simple docstring'''





											__magic_name__					=      LayoutLMForTokenClassification.from_pretrained('microsoft/layoutlm-base-uncased'	,      num_labels=1_3  ).to(
											    __lowerCAmelCase  )

											__magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__					=      prepare_layoutlm_batch_inputs()

											# forward pass
											__magic_name__					=      model(
											    input_ids=__lowerCAmelCase	,      bbox=__lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase	,      labels=__lowerCAmelCase  )

											# test the loss calculation to be around 2.65
											# expected_loss = torch.tensor(2.65, device=torch_device)

											# The loss is currently somewhat random and can vary between 0.1-0.3 atol.
											# self.assertTrue(torch.allclose(outputs.loss, expected_loss, atol=0.1))

											# test the shape of the logits
											__magic_name__					=      outputs.logits
											__magic_name__					=      torch.Size((2, 2_5, 1_3)  )
											self.assertEqual(logits.shape	,      __lowerCAmelCase  )







					@slow
					def 	a			(						self       :						Tuple  )							->					List[Any]:



											'''simple docstring'''





											__magic_name__					=      LayoutLMForQuestionAnswering.from_pretrained('microsoft/layoutlm-base-uncased'  ).to(__lowerCAmelCase  )

											__magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__		,      __magic_name__					=      prepare_layoutlm_batch_inputs()

											# forward pass
											__magic_name__					=      model(input_ids=__lowerCAmelCase	,      bbox=__lowerCAmelCase	,      attention_mask=__lowerCAmelCase	,      token_type_ids=__lowerCAmelCase  )

											# test the shape of the logits
											__magic_name__					=      torch.Size((2, 2_5)  )
											self.assertEqual(outputs.start_logits.shape	,      __lowerCAmelCase  )
											self.assertEqual(outputs.end_logits.shape	,      __lowerCAmelCase  )








from __future__ import annotations

def      a    (   _lowercase :  float | int			,    _lowercase :  float | int			,    _lowercase :  float | int			,    )  ->list[float | int]:
		if not all((nth_term, start_term_a, common_ratio_r)							):
				return []
		UpperCamelCase__								=						[]
		UpperCamelCase__								=						1
		UpperCamelCase__								=						common_ratio_r
		for _ in range(int(_lowercase							)							):
				if not series:
						series.append(_lowercase							)
				else:
						power += 1
						series.append(float(start_term_a * multiple							)							)
						UpperCamelCase__								=						pow(float(_lowercase							)			,    _lowercase							)
		return series


if __name__ == "__main__":
				import doctest

				doctest.testmod()

				__lowerCAmelCase 	=      float(input("Enter the last number (n term) of the Geometric Series"))
				__lowerCAmelCase 	=      float(input("Enter the starting term (a) of the Geometric Series"))
				__lowerCAmelCase 	=      float(
				    input("Enter the common ratio between two terms (r) of the Geometric Series")
				)
				print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
				print(geometric_series(nth_term, start_term_a, common_ratio_r))





