Abstract

We establish strict inequality bounds for the binomial sums $\sum_{i=0}^n {n\choose i} \frac{(-1)^i}{2i+1}$ and prove the asymptotic result: $$\sum_{i=0}^n {n\choose i} \frac{(-1)^i}{2i+1} \sim \sqrt{\frac{\pi}{2}} \frac{1}{\sqrt{2n+1}}, \mbox{ as } n\to \infty.$$

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