Created sum_of_harmonic_series.py (#7504)

* 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 !

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update maths/sum_of_harmonic_series.py

Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com>

* Update maths/sum_of_harmonic_series.py

Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com>

* Update maths/sum_of_harmonic_series.py

Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update maths/sum_of_harmonic_series.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update maths/sum_of_harmonic_series.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update maths/sum_of_harmonic_series.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update sum_of_harmonic_series.py

* Add doctests

* Update sum_of_harmonic_series.py

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 4 people

maths/sum_of_harmonic_series.py

@@ -0,0 +1,29 @@
+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))