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Created sum_of_harmonic_series.py (#7504)

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* Created sum_of_harmonic_series.py

Here in this code the formula for Harmonic sum is not used, Sum of the series is calculated by creating a list of the elements in the given Harmonic series and adding all the elements of that list !

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* Update maths/sum_of_harmonic_series.py

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def sum_of_harmonic_progression(
first_term: float, common_difference: float, number_of_terms: int
) -> float:
"""
https://en.wikipedia.org/wiki/Harmonic_progression_(mathematics)
Find the sum of n terms in an harmonic progression. The calculation starts with the
first_term and loops adding the common difference of Arithmetic Progression by which
the given Harmonic Progression is linked.
>>> sum_of_harmonic_progression(1 / 2, 2, 2)
0.75
>>> sum_of_harmonic_progression(1 / 5, 5, 5)
0.45666666666666667
"""
arithmetic_progression = [1 / first_term]
first_term = 1 / first_term
for _ in range(number_of_terms - 1):
first_term += common_difference
arithmetic_progression.append(first_term)
harmonic_series = [1 / step for step in arithmetic_progression]
return sum(harmonic_series)
if __name__ == "__main__":
import doctest
doctest.testmod()
print(sum_of_harmonic_progression(1 / 2, 2, 2))