Alternate harmonic series

maths/series/alternate_harmonic_series.py

@@ -0,0 +1,57 @@
+def is_alternate_harmonic_series(series: list) -> bool:
+    """
+    Web Biblography
+    https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
+
+    checking whether the input series is alternate harmonic series or not
+    >>> is_alternate_harmonic_series([1, -1/2, 1/3, -1/4, 1/5])
+    True
+    >>> is_alternate_harmonic_series([2/5, -2/10, 2/15, -2/20, 2/25])
+    True
+    >>> is_alternate_harmonic_series([1, 1/2, 1/3, 1/4])
+    False
+    >>> is_alternate_harmonic_series([1, -1/2, 1/4, -1/8])
+    False
+    >>> is_alternate_harmonic_series(4)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input series is not valid, valid series - [1, 2/3, 2]
+    >>> is_alternate_harmonic_series([])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input list must be a non empty list
+    >>> is_alternate_harmonic_series([0])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input series cannot have 0 as an element
+    >>> is_alternate_harmonic_series([1,2,0,6])
+    Traceback (most recent call last):
+        ...
+    ValueError: Input series cannot have 0 as an element
+    """
+    if not isinstance(series, list):
+        raise ValueError("Input series is not valid, valid series - [1, 2/3, 2]")
+    if len(series) == 0:
+        raise ValueError("Input list must be a non empty list")
+    if len(series) == 1 and series[0] != 0:
+        return True
+    receprocal = []
+    series_len = len(series)
+    for i in range(series_len):
+        if series[i] == 0:
+            raise ValueError("Input series cannot have 0 as an element")
+        receprocal.append(1 / series[i])
+    common_diff = abs(receprocal[1]) - abs(receprocal[0])
+    for index in range(2, series_len):
+        if (
+            abs(receprocal[index]) - abs(receprocal[index - 1]) != common_diff
+            or receprocal[index] * receprocal[index - 1] >= 0
+        ):
+            return False
+    return True
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()