query: Evaluate $\sum_{n=1}^{\infty}\frac{(-1)^n}{(2n+1)3^n}$
positive_passages.docid: 60288
positive_passages.text: Why is $\arctan(x)=x-x^3/3+x^5/5-x^7/7+\dots$?
negative_passages.docid: 49262
negative_passages.text: Evaluation of Sum of $ \sum_{n=1}^{\infty}\frac{\sin (n)}{n}$.
negative_passages.docid: 72502
negative_passages.text: Evaluate $\sum_{n=1}^\infty nx^{n-1}$
negative_passages.docid: 53658
negative_passages.text: Find the sum series $\sum_{n=1}^{+\infty} \frac{(-1)^{n-1}(2n-1)}{2^{n-1}}$
negative_passages.docid: 17332
negative_passages.text: How to compute $\sum\limits_{n=1}^{\infty}\frac{1}{x^n-1}$?
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: 66568
negative_passages.text: Number Theory : Show that $\sum_{i=0}^\infty$ $ [\frac{n}{2^i}+\frac{1}{2}]$ $=$ $2n$
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: 104078
negative_passages.text: Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$
negative_passages.docid: 138313
negative_passages.text: How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
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) $
negative_passages.docid: 54661
negative_passages.text: How to find the sum $\sum\limits_{n=1}^{\infty}\frac{1}{n!(n^4+n^2+1)}$
negative_passages.docid: 133955
negative_passages.text: Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$
negative_passages.docid: 64818
negative_passages.text: Use $\sum_{n=1}^\infty \frac{1}{n^4} = \frac{\pi^4}{90}$ to compute $\sum_{n=1}^\infty \frac{(-1)^n}{n^4}$
negative_passages.docid: 78542
negative_passages.text: What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$?
negative_passages.docid: 116723
negative_passages.text: Evaluating the sum $\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$
negative_passages.docid: 6416
negative_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?