A calculus problem by Sarth Vitekar

Calculus Level 5

\[\large \frac{1}{1} + \frac{1}{2} - \frac{2}{3} + \frac{1}{4} + \frac{1}{5} - \frac{2}{6} + \frac{1}{7} + \frac{1}{8} - \frac{2}{9} + \cdots = \ ? \]

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