


"""simple docstring"""







def _A						(						lowercase		):







    """simple docstring"""
    if n_term == "":
        return []
    a 		=[]
    for temp in range(int(lowercase		)		):
        series.append(f'''1/{temp + 1}''' if series else '''1'''		)
    return series


if __name__ == "__main__":
       lowerCamelCase_   :   Union[str, Any]									=  input("""Enter the last number (nth term) of the Harmonic Series""")
       print("""Formula of Harmonic Series => 1+1/2+1/3 ..... 1/n""")
       print(harmonic_series(nth_term))




'''simple docstring'''






from math import cos, sin, sqrt, tau

from audio_filters.iir_filter import IIRFilter


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Optional[int] 							=		tau * frequency / samplerate
							UpperCAmelCase :       List[Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[Any] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       int 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       Any 							=		(1 - _cos) / 2
							UpperCAmelCase :       List[Any] 							=		1 - _cos

							UpperCAmelCase :       Union[str, Any] 							=		1 + alpha
							UpperCAmelCase :       Any 							=		-2 * _cos
							UpperCAmelCase :       Dict 							=		1 - alpha

							UpperCAmelCase :       Union[str, Any] 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Any 							=		tau * frequency / samplerate
							UpperCAmelCase :       Tuple 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Tuple 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Dict 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       int 							=		(1 + _cos) / 2
							UpperCAmelCase :       List[Any] 							=		-1 - _cos

							UpperCAmelCase :       Tuple 							=		1 + alpha
							UpperCAmelCase :       List[str] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha

							UpperCAmelCase :       Tuple 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       Optional[int] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Optional[int] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Tuple 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[int] 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       Union[str, Any] 							=		_sin / 2
							UpperCAmelCase :       Any 							=		0
							UpperCAmelCase :       int 							=		-ba

							UpperCAmelCase :       Optional[Any] 							=		1 + alpha
							UpperCAmelCase :       List[Any] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha

							UpperCAmelCase :       int 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )  )      ->   IIRFilter:
							UpperCAmelCase :       List[str] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Union[str, Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       str 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[Any] 							=		_sin / (2 * q_factor)

							UpperCAmelCase :       List[str] 							=		1 - alpha
							UpperCAmelCase :       Any 							=		-2 * _cos
							UpperCAmelCase :       Optional[int] 							=		1 + alpha

							UpperCAmelCase :       Union[str, Any] 							=		IIRFilter(2  )
							filt.set_coefficients([ba, ba, ba]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )   ,      )      ->   IIRFilter:
							UpperCAmelCase :       Optional[Any] 							=		tau * frequency / samplerate
							UpperCAmelCase :       Union[str, Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Optional[int] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Dict 							=		_sin / (2 * q_factor)
							UpperCAmelCase :       str 							=		10 ** (gain_db / 40)

							UpperCAmelCase :       int 							=		1 + alpha * big_a
							UpperCAmelCase :       Union[str, Any] 							=		-2 * _cos
							UpperCAmelCase :       Optional[Any] 							=		1 - alpha * big_a
							UpperCAmelCase :       Union[str, Any] 							=		1 + alpha / big_a
							UpperCAmelCase :       Tuple 							=		-2 * _cos
							UpperCAmelCase :       Any 							=		1 - alpha / big_a

							UpperCAmelCase :       Optional[Any] 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt


def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )   ,      )      ->   IIRFilter:
							UpperCAmelCase :       Any 							=		tau * frequency / samplerate
							UpperCAmelCase :       Optional[int] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Union[str, Any] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       str 							=		_sin / (2 * q_factor)
							UpperCAmelCase :       List[str] 							=		10 ** (gain_db / 40)
							UpperCAmelCase :       Optional[int] 							=		(big_a + 1) - (big_a - 1) * _cos
							UpperCAmelCase :       int 							=		(big_a + 1) + (big_a - 1) * _cos
							UpperCAmelCase :       int 							=		(big_a - 1) - (big_a + 1) * _cos
							UpperCAmelCase :       Optional[int] 							=		(big_a - 1) + (big_a + 1) * _cos
							UpperCAmelCase :       str 							=		2 * sqrt(_lowerCAmelCase  ) * alpha

							UpperCAmelCase :       Dict 							=		big_a * (pmc + aaa)
							UpperCAmelCase :       Any 							=		2 * big_a * mpc
							UpperCAmelCase :       Union[str, Any] 							=		big_a * (pmc - aaa)
							UpperCAmelCase :       Optional[int] 							=		ppmc + aaa
							UpperCAmelCase :       Optional[Any] 							=		-2 * pmpc
							UpperCAmelCase :       Optional[Any] 							=		ppmc - aaa

							UpperCAmelCase :       int 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt




def  snake_case_     (					_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						float   ,      _lowerCAmelCase  :						float = 1 / sqrt(2  )   ,      )      ->   IIRFilter:
							UpperCAmelCase :       int 							=		tau * frequency / samplerate
							UpperCAmelCase :       Union[str, Any] 							=		sin(_lowerCAmelCase  )
							UpperCAmelCase :       Union[str, Any] 							=		cos(_lowerCAmelCase  )
							UpperCAmelCase :       Any 							=		_sin / (2 * q_factor)
							UpperCAmelCase :       int 							=		10 ** (gain_db / 40)
							UpperCAmelCase :       List[str] 							=		(big_a + 1) - (big_a - 1) * _cos
							UpperCAmelCase :       Union[str, Any] 							=		(big_a + 1) + (big_a - 1) * _cos
							UpperCAmelCase :       Optional[Any] 							=		(big_a - 1) - (big_a + 1) * _cos
							UpperCAmelCase :       Union[str, Any] 							=		(big_a - 1) + (big_a + 1) * _cos
							UpperCAmelCase :       List[str] 							=		2 * sqrt(_lowerCAmelCase  ) * alpha

							UpperCAmelCase :       Any 							=		big_a * (ppmc + aaa)
							UpperCAmelCase :       str 							=		-2 * big_a * pmpc
							UpperCAmelCase :       List[Any] 							=		big_a * (ppmc - aaa)
							UpperCAmelCase :       Optional[Any] 							=		pmc + aaa
							UpperCAmelCase :       Any 							=		2 * mpc
							UpperCAmelCase :       str 							=		pmc - aaa

							UpperCAmelCase :       Union[str, Any] 							=		IIRFilter(2  )
							filt.set_coefficients([aa, aa, aa]   ,      [ba, ba, ba]  )
							return filt





