query: How to solve infinite series $\sum_{n=0}^\infty\frac{n}{2^{(n+1)}}$?
positive_passages.docid: 6416
positive_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 66568
negative_passages.text: Number Theory : Show that $\sum_{i=0}^\infty$ $ [\frac{n}{2^i}+\frac{1}{2}]$ $=$ $2n$
negative_passages.docid: 65653
negative_passages.text: Find a closed form of the series $\sum_{n=0}^{\infty} n^2x^n$
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: 16967
negative_passages.text: Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$
negative_passages.docid: 93690
negative_passages.text: How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
negative_passages.docid: 47980
negative_passages.text: Infinite series $\sum _{n=2}^{\infty } \frac{1}{n \log (n)}$
negative_passages.docid: 137027
negative_passages.text: Find the value of $\sum_{n=0}^\infty\frac{1}{9n^2+9n+2}$
negative_passages.docid: 104646
negative_passages.text: Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 43320
negative_passages.text: Find the sum of the power series $\sum_{n=1}^\infty n*(n+1)*x^n$
negative_passages.docid: 136444
negative_passages.text: Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
negative_passages.docid: 326
negative_passages.text: Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
negative_passages.docid: 117863
negative_passages.text: Series $\sum_{n=1}^\infty \frac{n^n}{(n!)^2}$
negative_passages.docid: 125915
negative_passages.text: An Infinite Double Summation $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{n^2k^2(n+k)^2}$?
negative_passages.docid: 92690
negative_passages.text: Infinite Series $\sum\limits_{n=0}^{\infty}\arctan(\frac{1}{F_{2n+1}})$
negative_passages.docid: 67731
negative_passages.text: Calculate the sum of infinite series with general term $\frac{n^2}{2^n}$.