





def 							lowerCAmelCase_				(    A_):



    if not isinstance(A_  ,A_):
        raise ValueError("Input series is not valid, valid series - [2, 4, 8]")
    if len(A_) == 0:
        raise ValueError("Input list must be a non empty list")
    if len(A_) == 1:
        return True
    try:
        UpperCamelCase__:					Union[str, Any]												=      series[1] / series[0]
        for index in range(len(A_) - 1):
            if series[index + 1] / series[index] != common_ratio:
                return False
    except ZeroDivisionError:
        return False
    return True



def 							lowerCAmelCase_				(    A_):



    if not isinstance(A_  ,A_):
        raise ValueError("Input series is not valid, valid series - [2, 4, 8]")
    if len(A_) == 0:
        raise ValueError("Input list must be a non empty list")
    UpperCamelCase__:					List[Any]												=      1
    for value in series:
        answer *= value
    return pow(A_  ,1 / len(A_))


if __name__ == "__main__":
   import doctest

   doctest.testmod()








def 							lowerCAmelCase_				(    A_  ,A_  ,A_):
    UpperCamelCase__:					Optional[int]												=      [1 / first_term]
    UpperCamelCase__:					int												=      1 / first_term
    for _ in range(number_of_terms - 1):
        first_term += common_difference
        arithmetic_progression.append(A_)
    UpperCamelCase__:					str												=      [1 / step for step in arithmetic_progression]
    return sum(A_)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   print(sum_of_harmonic_progression(1 / 2, 2, 2))

