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CalculusChallengeInfinite Sequences and Series

Infinite Sequences and Series · Challenge problem

Find the exact value of ∑n=0∞(−1)n(2n+1) 3n=1−13⋅3+15⋅9−17⋅27+⋯\displaystyle\sum_{n=0}^{\infty}\frac{(-1)^n}{(2n+1)\,3^n}=1-\frac{1}{3\cdot3}+\frac{1}{5\cdot9}-\frac{1}{7\cdot27}+\cdots.