Some Inequalities and Asymptotics for a Weighted Alternate Binomial Sum
- J. C. S. de Miranda
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: $$\sum_{i=0}^n {n\choose i} \frac{(-1)^i}{2i+1} \sim \sqrt{\frac{\pi}{2}} \frac{1}{\sqrt{2n+1}}, \mbox{ as } n\to \infty.$$- Full Text:
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- DOI:10.5539/jmr.v4n3p61
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