geometric series are used throughout mathematics, and they have important applications in physics, technology, biology, economics, computer science, queueing theory, and finance. Historically, geometric series played an important character in the early development of calculus, and they continue to be central in the survey of convergence of series.

COMING SOON!

```
"""
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)
[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))
```