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CalculusSuperchallengeInfinite Sequences and Series

Infinite Sequences and Series · Superchallenge problem

Find the exact value of ∑n=0∞(−1)n3n+1=1−14+17−110+⋯\displaystyle\sum_{n=0}^{\infty}\frac{(-1)^n}{3n+1}=1-\frac14+\frac17-\frac1{10}+\cdots.