


from __future__ import annotations






def 							__lowercase     (				__lowerCAmelCase							:       list[float]     ):
							a__    =  0.00
							a__    =  0
							for resistor in resistors:
														if resistor <= 0:
																					a__    =  F'Resistor at index {index} has a negative or zero value!'
																					raise ValueError(__lowerCAmelCase     )
														first_sum += 1 / float(__lowerCAmelCase     )
														index += 1
							return 1 / first_sum






def 							__lowercase     (				__lowerCAmelCase							:       list[float]     ):
							a__    =  0.00
							a__    =  0
							for resistor in resistors:
														sum_r += resistor
														if resistor < 0:
																					a__    =  F'Resistor at index {index} has a negative value!'
																					raise ValueError(__lowerCAmelCase     )
														index += 1
							return sum_r


if __name__ == "__main__":
						import doctest

						doctest.testmod()








from decimal import Decimal, getcontext
from math import ceil, factorial






def 							__lowercase     (				__lowerCAmelCase							:       int     ):

							if not isinstance(__lowerCAmelCase      ,					__lowerCAmelCase     ):
														raise TypeError('Undefined for non-integers'     )
							elif precision < 1:
														raise ValueError('Undefined for non-natural numbers'     )

							a__    =  precision
							a__    =  ceil(precision / 1_4     )
							a__    =  4_2_6_8_8_0 * Decimal(1_0_0_0_5     ).sqrt()
							a__    =  1
							a__    =  1_3_5_9_1_4_0_9
							a__    =  Decimal(__lowerCAmelCase     )
							for k in range(1      ,					__lowerCAmelCase     ):
														a__    =  factorial(6 * k     ) // (factorial(3 * k     ) * factorial(__lowerCAmelCase     ) ** 3)
														linear_term += 5_4_5_1_4_0_1_3_4
														exponential_term *= -2_6_2_5_3_7_4_1_2_6_4_0_7_6_8_0_0_0
														partial_sum += Decimal(multinomial_term * linear_term     ) / exponential_term
							return str(constant_term / partial_sum     )[:-1]


if __name__ == "__main__":
						snake_case							: Tuple      =   50
						print(f"""The first {n} digits of pi is: {pi(n)}""")




