Harmonic Geometric and P-Series Added (TheAlgorithms#1633)

* Harmonic Geometric and P-Series Added

* Editing comments

* Update and rename series/Geometric_Series.py to maths/series/geometric_series.py

* Update and rename series/Harmonic_Series.py to maths/series/harmonic_series.py

* Update and rename series/P_Series.py to maths/series/p_series.py

Author: MeIbtihajnaeem

maths/series/geometric_series.py

@@ -0,0 +1,63 @@
+"""
+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))

maths/series/harmonic_series.py

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+"""
+This is a pure Python implementation of the Harmonic Series algorithm
+https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
+
+For doctests run following command:
+python -m doctest -v harmonic_series.py
+or
+python3 -m doctest -v harmonic_series.py
+
+For manual testing run:
+python3 harmonic_series.py
+"""
+
+
+def harmonic_series(n_term: str) -> list:
+    """Pure Python implementation of Harmonic Series algorithm
+
+    :param n_term: The last (nth) term of Harmonic Series
+    :return: The Harmonic Series starting from 1 to last (nth) term
+
+    Examples:
+    >>> harmonic_series(5)
+    ['1', '1/2', '1/3', '1/4', '1/5']
+    >>> harmonic_series(5.0)
+    ['1', '1/2', '1/3', '1/4', '1/5']
+    >>> harmonic_series(5.1)
+    ['1', '1/2', '1/3', '1/4', '1/5']
+    >>> harmonic_series(-5)
+    []
+    >>> harmonic_series(0)
+    []
+    >>> harmonic_series(1)
+    ['1']
+    """
+    if n_term == "":
+        return n_term
+    series = []
+    for temp in range(int(n_term)):
+        series.append(f"1/{temp + 1}" if series else "1")
+    return series
+
+
+if __name__ == "__main__":
+    nth_term = input("Enter the last number (nth term) of the Harmonic Series")
+    print("Formula of Harmonic Series => 1+1/2+1/3 ..... 1/n")
+    print(harmonic_series(nth_term))

maths/series/p_series.py

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+"""
+This is a pure Python implementation of the P-Series algorithm
+https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)#P-series
+
+For doctests run following command:
+python -m doctest -v p_series.py
+or
+python3 -m doctest -v p_series.py
+
+For manual testing run:
+python3 p_series.py
+"""
+
+
+def p_series(nth_term: int, power: int) -> list:
+    """Pure Python implementation of P-Series algorithm
+
+    :return: The P-Series starting from 1 to last (nth) term
+
+    Examples:
+    >>> p_series(5, 2)
+    [1, '1/4', '1/9', '1/16', '1/25']
+    >>> p_series(-5, 2)
+    []
+    >>> p_series(5, -2)
+    [1, '1/0.25', '1/0.1111111111111111', '1/0.0625', '1/0.04']
+    >>> p_series("", 1000)
+    ''
+    >>> p_series(0, 0)
+    []
+    >>> p_series(1, 1)
+    [1]
+    """
+    if nth_term == "":
+        return nth_term
+    nth_term = int(nth_term)
+    power = int(power)
+    series = []
+    for temp in range(int(nth_term)):
+        series.append(f"1/{pow(temp + 1, int(power))}" if series else 1)
+    return series
+
+
+if __name__ == "__main__":
+    nth_term = input("Enter the last number (nth term) of the P-Series")
+    power = input("Enter the power for  P-Series")
+    print("Formula of P-Series => 1+1/2^p+1/3^p ..... 1/n^p")
+    print(p_series(nth_term, power))