




"""simple docstring"""







def 							lowercase   (snake_case__				:	list	)       ->					bool:


				'''simple docstring'''






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





def 							lowercase   (snake_case__				:	list	)       ->					float:


				'''simple docstring'''






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


if __name__ == "__main__":
		import doctest

		doctest.testmod()











"""simple docstring"""







def 							lowercase   (snake_case__				:	list	)       ->					bool:


				'''simple docstring'''






				if not isinstance(snake_case__ ,    snake_case__	):
								raise ValueError("""Input series is not valid, valid series - [1, 2/3, 2]"""	)
				if len(snake_case__	) == 0:
								raise ValueError("""Input list must be a non empty list"""	)
				if len(snake_case__	) == 1 and series[0] != 0:
								return True
				lowerCAmelCase		=			[]
				lowerCAmelCase		=			len(snake_case__	)
				for i in range(0 ,    snake_case__	):
								if series[i] == 0:
												raise ValueError("""Input series cannot have 0 as an element"""	)
								rec_series.append(1 / series[i]	)
				lowerCAmelCase		=			rec_series[1] - rec_series[0]
				for index in range(2 ,    snake_case__	):
								if rec_series[index] - rec_series[index - 1] != common_diff:
												return False
				return True





def 							lowercase   (snake_case__				:	list	)       ->					float:


				'''simple docstring'''






				if not isinstance(snake_case__ ,    snake_case__	):
								raise ValueError("""Input series is not valid, valid series - [2, 4, 6]"""	)
				if len(snake_case__	) == 0:
								raise ValueError("""Input list must be a non empty list"""	)
				lowerCAmelCase		=			0
				for val in series:
								answer += 1 / val
				return len(snake_case__	) / answer


if __name__ == "__main__":
		import doctest

		doctest.testmod()





