"""simple docstring"""







def   __UpperCAmelCase    (   UpperCAmelCase_   :    int      ,							UpperCAmelCase_   :    int      ,							UpperCAmelCase_   :    int  )							->      float:

	'''simple docstring'''





	__snake_case      :							Union[str, Any]						=			(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
	# formula for sum of series
	return total
def   __UpperCAmelCase    (   )							->      Optional[int]:

	'''simple docstring'''





	print(sum_of_series(1      ,							1      ,							10  )  )


if __name__ == "__main__":
	import doctest

	doctest.testmod()






"""simple docstring"""







from decimal import Decimal, getcontext
from math import ceil, factorial
def   __UpperCAmelCase    (   UpperCAmelCase_   :    int  )							->      str:

	'''simple docstring'''





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

	__snake_case      :							Any						=			precision
	__snake_case      :							Optional[int]						=			ceil(precision / 14  )
	__snake_case      :							List[Any]						=			42_68_80 * Decimal(1_00_05  ).sqrt()
	__snake_case      :							Optional[Any]						=			1
	__snake_case      :							Union[str, Any]						=			13_59_14_09
	__snake_case      :							int						=			Decimal(UpperCAmelCase_  )
	for k in range(1      ,							UpperCAmelCase_  ):
		__snake_case      :							Union[str, Any]						=			factorial(6 * k  ) // (factorial(3 * k  ) * factorial(UpperCAmelCase_  ) ** 3)
		linear_term += 5_45_14_01_34
		exponential_term *= -26_25_37_41_26_40_76_80_00
		partial_sum += Decimal(multinomial_term * linear_term  ) / exponential_term
	return str(constant_term / partial_sum  )[:-1]


if __name__ == "__main__":
	_a					:					List[Any]=			50
	print(f'''The first {n} digits of pi is: {pi(n)}''')





