




'''simple docstring'''


from __future__ import annotations
def 						lowerCamelCase__   (				a    ,	a							):
						if nth_term == "":
												return [""]
						__snake_case						 =   int(a							)
						__snake_case						 =   int(a							)
						__snake_case						 =   []
						for temp in range(int(a							)							):
												series.append(f'1 / {pow(temp + 1    ,	int(a							)							)}' if series else '1'							)
						return series


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	_lowercase  =			int(input("""Enter the last number (nth term) of the P-Series"""))
	_lowercase  =			int(input("""Enter the power for  P-Series"""))
	print("""Formula of P-Series => 1+1/2^p+1/3^p ..... 1/n^p""")
	print(p_series(nth_term, power))







'''simple docstring'''


from __future__ import annotations

import math
def 						lowerCamelCase__   (				a    ,	a							):
						__snake_case						 =   u
						for i in range(1    ,	a							):
												__snake_case						 =   temp * (u - i)
						return temp
def 						lowerCamelCase__   (				):
						__snake_case						 =   int(input('enter the numbers of values: '							)							)
						__snake_case						 =   []
						for _ in range(a							):
												y.append([]							)
						for i in range(a							):
												for j in range(a							):
																		y[i].append(a							)
																		__snake_case						 =   0

						print('enter the values of parameters in a list: '							)
						__snake_case						 =   list(map(a    ,	input().split()							)							)

						print('enter the values of corresponding parameters: '							)
						for i in range(a							):
												__snake_case						 =   float(input()							)

						__snake_case						 =   int(input('enter the value to interpolate: '							)							)
						__snake_case						 =   (value - x[0]) / (x[1] - x[0])

						# for calculating forward difference table

						for i in range(1    ,	a							):
												for j in range(n - i							):
																		__snake_case						 =   y[j + 1][i - 1] - y[j][i - 1]

						__snake_case						 =   y[0][0]
						for i in range(1    ,	a							):
												summ += (ucal(a    ,	a							) * y[0][i]) / math.factorial(a							)

						print(f'the value at {value} is {summ}'							)


if __name__ == "__main__":
	main()

