♔Renascence_5

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

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

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