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"""

This is a pure Python implementation of the P-Series algorithm

https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#P-series

For doctests run following command:

python -m doctest -v p_series.py

python3 -m doctest -v p_series.py

For manual testing run:

python3 p_series.py

"""

def p_series(nth_term: int, power: int) -> list:

"""Pure Python implementation of P-Series algorithm

:return: The P-Series starting from 1 to last (nth) term

Examples:

>>> p_series(5, 2)

[1, '1/4', '1/9', '1/16', '1/25']

>>> p_series(-5, 2)

[]

>>> p_series(5, -2)

[1, '1/0.25', '1/0.1111111111111111', '1/0.0625', '1/0.04']

>>> p_series("", 1000)

>>> p_series(0, 0)

[]

>>> p_series(1, 1)

[1]

"""

if nth_term == "":

return nth_term

nth_term = int(nth_term)

power = int(power)

series = []

for temp in range(int(nth_term)):

series.append(f"1/{pow(temp + 1, int(power))}" if series else 1)

return series

if __name__ == "__main__":

nth_term = input("Enter the last number (nth term) of the P-Series")

power = 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))

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