query: Calculation of $\sum_{m=1}^{\infty}\sum_{n=1}^{\infty}\frac{m^2n}{3^n\left(m\cdot 3^n+n\cdot 3^m\right)}$
positive_passages.docid: 140008
positive_passages.text: I need help with a double sum
negative_passages.docid: 41366
negative_passages.text: Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$
negative_passages.docid: 135927
negative_passages.text: Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$
negative_passages.docid: 122445
negative_passages.text: Sum of the series:$\frac{1}{1\cdot 2}+\frac{1\cdot3}{1\cdot2\cdot3\cdot4}+\cdots$
negative_passages.docid: 18397
negative_passages.text: Factorial sum estimate $\sum_{n=m+1}^\infty \frac{1}{n!} \le \frac{1}{m\cdot m!}$
negative_passages.docid: 136444
negative_passages.text: Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
negative_passages.docid: 86900
negative_passages.text: Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum
negative_passages.docid: 136066
negative_passages.text: Find the sum $\sum _{n=1}^{\infty }\left(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n}\right)$
negative_passages.docid: 104646
negative_passages.text: Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
negative_passages.docid: 14223
negative_passages.text: Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$
negative_passages.docid: 89698
negative_passages.text: Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
negative_passages.docid: 7177
negative_passages.text: Find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $
negative_passages.docid: 55061
negative_passages.text: Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
negative_passages.docid: 913
negative_passages.text: Evaluating $\sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}$
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 725
negative_passages.text: proof of $\sum_{n=1}^\infty n \cdot x^n= \frac{x}{(x-1)^2}$
negative_passages.docid: 94143
negative_passages.text: Evaluate:: $ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right) $