query: Find the sum of the series $\sum _{n=1}^{\infty }\left(\frac{n+1}{2^n}\right)$
positive_passages.docid: 6416
positive_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 44754
negative_passages.text: Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{4^n\cos^2\frac{x}{2^n}}$
negative_passages.docid: 138313
negative_passages.text: How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
negative_passages.docid: 35036
negative_passages.text: Series $\sum_{n=1}^{\infty}\frac{\cos(nx)}{n^2}$
negative_passages.docid: 50812
negative_passages.text: Partial sum of the series $\sum\limits_{r=1}^{\infty} \frac{1}{r(r+1)}$
negative_passages.docid: 59485
negative_passages.text: Infinite Series: $\sum_{n=1}^\infty \frac{1}{2^nn}$
negative_passages.docid: 134576
negative_passages.text: Does this series converge or diverge? $\sum_{n=1}^\infty\ln\left(1+\frac1{n^2}\right)$
negative_passages.docid: 33986
negative_passages.text: Calculate $\sum_{n=1}^{\infty}(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2n+4})$
negative_passages.docid: 22636
negative_passages.text: Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
negative_passages.docid: 74120
negative_passages.text: Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
negative_passages.docid: 14883
negative_passages.text: Find $\sum_{n=1}^{\infty}$ $\frac{n^{2}}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\left(n+4\right)}$
negative_passages.docid: 127189
negative_passages.text: sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$
negative_passages.docid: 91316
negative_passages.text: Sum of the series $\sum _{ r=1 }^{ \infty }{ \frac { { r }^{ 3 } }{ r! } } $
negative_passages.docid: 74117
negative_passages.text: Find the sum of series $\sum_{n=0}^{\infty}\frac{z^{kn}}{(kn)!}$
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 32866
negative_passages.text: How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
negative_passages.docid: 55339
negative_passages.text: Find the sum $\sum_{n=1}^{\infty}\frac{ 1}{n^{2}(2n-1)}$