摘要:$$\Large\displaystyle \sum_{n=1}^{\infty}\frac{H_{2n}}{n(6n+1)}$$ $\Large\mathbf{Solution:}$ Let $S$ denote the sum. Then $$\begin{align } S=\sum_{n=1 阅读全文
posted @ 2016-05-12 16:24 Renascence_5 阅读(430) 评论(0) 推荐(0) 编辑
摘要:$$\Large\displaystyle \sum_{n=1}^{\infty} \frac{\widetilde{H_n}}{n^{3}}$$ where $\widetilde{H_n}$ is the alternating harmonic number. $\Large\mathbf{S 阅读全文
posted @ 2016-05-12 16:09 Renascence_5 阅读(418) 评论(0) 推荐(0) 编辑
摘要:$$\sum_{n = 1}^\infty {\frac{1}{{{n^3}}}} \left( {\sum\limits_{k = 1}^n {\frac{{{{\left( { 1} \right)}^{k 1}}}}{k}} } \right) = \frac{7}{4}\zeta \left 阅读全文
posted @ 2016-05-12 15:40 Renascence_5 阅读(323) 评论(0) 推荐(0) 编辑