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CalculusHardInfinite Sequences and Series

Infinite Sequences and Series · Hard problem

Find the exact sum of ∑n=0∞(−1)n π2n+162n+1 (2n+1)!\displaystyle\sum_{n=0}^{\infty}\frac{(-1)^n\,\pi^{2n+1}}{6^{2n+1}\,(2n+1)!}.