Add alternating harmonic series checker (#14634)

* Add alternating harmonic series checker

* Add reference link for alternating harmonic series

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

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

maths/series/alternating_harmonic_series.py

@@ -0,0 +1,34 @@
+"""Alternating Harmonic Series Checker"""
+# https://en.wikipedia.org/wiki/Alternating_harmonic_series
+
+
+def is_alternate_harmonic_series(series: list) -> bool:
+    """
+    Returns True if the given series is an Alternating Harmonic Series.
+
+    Examples:
+    >>> is_alternate_harmonic_series([1, -1/2, 1/3, -1/4])
+    True
+
+    >>> is_alternate_harmonic_series([1, 1/2, 1/3])
+    False
+
+    >>> is_alternate_harmonic_series([])
+    False
+    """
+
+    if not series:
+        return False
+
+    for i, value in enumerate(series):
+        expected = ((-1) ** i) * (1 / (i + 1))
+
+        if abs(value - expected) > 1e-9:
+            return False
+
+    return True
+
+
+if __name__ == "__main__":
+    sample = [1, -1 / 2, 1 / 3, -1 / 4]
+    print(is_alternate_harmonic_series(sample))