Re-organize math/series (#5044)

* added harmonic mean

* Update maths/series/harmonic_mean.py

Updated the write-up of reference given in the code.

Co-authored-by: John Law <johnlaw.po@gmail.com>

* changes in arithmetic and geometric mean code

* mean and series added in a single file

Co-authored-by: John Law <johnlaw.po@gmail.com>

maths/series/geometric.py

@@ -0,0 +1,83 @@
+"""
+Geometric Mean
+Reference :  https://en.wikipedia.org/wiki/Geometric_mean
+
+Geometric series
+Reference: https://en.wikipedia.org/wiki/Geometric_series
+"""
+
+
+def is_geometric_series(series: list) -> bool:
+    """
+    checking whether the input series is geometric series or not
+    >>> is_geometric_series([2, 4, 8])
+    True
+    >>> is_geometric_series([3, 6, 12, 24])
+    True
+    >>> is_geometric_series([1, 2, 3])
+    False
+    >>> is_geometric_series([0, 0, 3])
+    False
+    >>> is_geometric_series([])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list must be a non empty list
+    >>> is_geometric_series(4)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input series is not valid, valid series - [2, 4, 8]
+    """
+    if not isinstance(series, list):
+        raise ValueError("Input series is not valid, valid series - [2, 4, 8]")
+    if len(series) == 0:
+        raise ValueError("Input list must be a non empty list")
+    if len(series) == 1:
+        return True
+    try:
+        common_ratio = series[1] / series[0]
+        for index in range(len(series) - 1):
+            if series[index + 1] / series[index] != common_ratio:
+                return False
+    except ZeroDivisionError:
+        return False
+    return True
+
+
+def geometric_mean(series: list) -> float:
+    """
+    return the geometric mean of series
+
+    >>> geometric_mean([2, 4, 8])
+    3.9999999999999996
+    >>> geometric_mean([3, 6, 12, 24])
+    8.48528137423857
+    >>> geometric_mean([4, 8, 16])
+    7.999999999999999
+    >>> geometric_mean(4)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input series is not valid, valid series - [2, 4, 8]
+    >>> geometric_mean([1, 2, 3])
+    1.8171205928321397
+    >>> geometric_mean([0, 2, 3])
+    0.0
+    >>> geometric_mean([])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list must be a non empty list
+
+    """
+    if not isinstance(series, list):
+        raise ValueError("Input series is not valid, valid series - [2, 4, 8]")
+    if len(series) == 0:
+        raise ValueError("Input list must be a non empty list")
+    answer = 1
+    for value in series:
+        answer *= value
+    return pow(answer, 1 / len(series))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()