query: Find the sum of an infinite series for the following series
positive_passages.docid: 6416
positive_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 151477
negative_passages.text: computing the series $\sum_{n=1}^\infty \frac{1}{n^2 2^n}$
negative_passages.docid: 81589
negative_passages.text: Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
negative_passages.docid: 35036
negative_passages.text: Series $\sum_{n=1}^{\infty}\frac{\cos(nx)}{n^2}$
negative_passages.docid: 45588
negative_passages.text: Summing a series with a changing power
negative_passages.docid: 94943
negative_passages.text: Sum of series with addition: $\sum_{n=1}^\infty \frac{1}{n^2(n+1)}$
negative_passages.docid: 94871
negative_passages.text: Sum of an unorthodox infinite series
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: 32637
negative_passages.text: What is the sum of this series: $\displaystyle\sum_{n=0}^{\infty} \dfrac{a^n}{(3n)!}$
negative_passages.docid: 86194
negative_passages.text: Infinite series with the binomial coefficient
negative_passages.docid: 58262
negative_passages.text: Find the sum of the series $1+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{5}\cdot\frac{1}{4^2}+\frac{1}{7}\cdot\frac{1}{4^3}+\cdots$
negative_passages.docid: 51146
negative_passages.text: Sum of Infinite Series $1 + 1/2 + 1/4 + 1/16 + \cdots$
negative_passages.docid: 101052
negative_passages.text: Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
negative_passages.docid: 30895
negative_passages.text: Compute the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$
negative_passages.docid: 47596
negative_passages.text: An infinite series plus a continued fraction by Ramanujan
negative_passages.docid: 14223
negative_passages.text: Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$
negative_passages.docid: 92665
negative_passages.text: Find a function for the infinite sum $\sum_{n=0}^\infty \frac{n}{n+1}x^n$