``````"""
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
"""

def geometric_series(nth_term: int, start_term_a: int, common_ratio_r: int) -> list:
"""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 "" in (nth_term, start_term_a, common_ratio_r):
return ""
series = []
power = 1
multiple = common_ratio_r
for _ in range(int(nth_term)):
if series == []:
series.append(start_term_a)
else:
power += 1
series.append(str(float(start_term_a) * float(multiple)))
multiple = pow(float(common_ratio_r), power)
return series

if __name__ == "__main__":
nth_term = input("Enter the last number (n term) of the Geometric Series")
start_term_a = input("Enter the starting term (a) of the Geometric Series")
common_ratio_r = 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))
``````

#### Geometric Series

M  