#### Geometric Series

```"""
This is a pure Python implementation of the Geometric Series algorithm
https://en.wikipedia.org/wiki/Geometric_series
Run the doctests with the following command:
python3 -m doctest -v geometric_series.py
or
python -m doctest -v geometric_series.py
For manual testing run:
python3 geometric_series.py
"""

from __future__ import annotations

def geometric_series(
nth_term: float | int,
start_term_a: float | int,
common_ratio_r: float | int,
) -> list[float | int]:
"""
Pure Python implementation of Geometric Series algorithm

:param nth_term: The last term (nth term of Geometric Series)
:param start_term_a : The first term of Geometric Series
:param common_ratio_r : The common ratio between all the terms
:return: The Geometric Series starting from first term a and multiple of common
ration with first term with increase in power till last term (nth term)
Examples:
>>> geometric_series(4, 2, 2)
[2, 4.0, 8.0, 16.0]
>>> geometric_series(4.0, 2.0, 2.0)
[2.0, 4.0, 8.0, 16.0]
>>> geometric_series(4.1, 2.1, 2.1)
[2.1, 4.41, 9.261000000000001, 19.448100000000004]
>>> geometric_series(4, 2, -2)
[2, -4.0, 8.0, -16.0]
>>> geometric_series(4, -2, 2)
[-2, -4.0, -8.0, -16.0]
>>> geometric_series(-4, 2, 2)
[]
>>> geometric_series(0, 100, 500)
[]
>>> geometric_series(1, 1, 1)

>>> geometric_series(0, 0, 0)
[]
"""
if not all((nth_term, start_term_a, common_ratio_r)):
return []
series: list[float | int] = []
power = 1
multiple = common_ratio_r
for _ in range(int(nth_term)):
if series == []:
series.append(start_term_a)
else:
power += 1
series.append(float(start_term_a * multiple))
multiple = pow(float(common_ratio_r), power)
return series

if __name__ == "__main__":
import doctest

doctest.testmod()

nth_term = float(input("Enter the last number (n term) of the Geometric Series"))
start_term_a = float(input("Enter the starting term (a) of the Geometric Series"))
common_ratio_r = float(
input("Enter the common ratio between two terms (r) of the Geometric Series")
)
print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
print(geometric_series(nth_term, start_term_a, common_ratio_r))
```  