query: Evaluating $\sum_{r=0}^{n}\frac{(-1)^r}{(r+1)^2}{n\choose r}$
positive_passages.docid: 146762
positive_passages.text: Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
negative_passages.docid: 114911
negative_passages.text: Evaluate $\sum_{k = 0}^{n} {n\choose k} k^m$
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: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 63879
negative_passages.text: Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
negative_passages.docid: 562
negative_passages.text: Formula for calculating $\sum_{n=0}^{m}nr^n$
negative_passages.docid: 104365
negative_passages.text: Evaluate: $\lim_{n\to\infty}\left({2\sqrt n}-\sum_{k=1}^n\frac1{\sqrt k}\right)$
negative_passages.docid: 131326
negative_passages.text: How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
negative_passages.docid: 146533
negative_passages.text: Having problems proving $ \sum_{r=0}^{n}(r+1) \binom{n}{r} = (n+2)2^{n-1} $
negative_passages.docid: 96961
negative_passages.text: A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
negative_passages.docid: 140877
negative_passages.text: Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
negative_passages.docid: 37650
negative_passages.text: Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
negative_passages.docid: 108010
negative_passages.text: Evaluating $\sum_{k=1}^{\infty}\left(\frac{\sin(tk)}{k}\right)^2$
negative_passages.docid: 114031
negative_passages.text: Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
negative_passages.docid: 151757
negative_passages.text: Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
negative_passages.docid: 39909
negative_passages.text: Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
negative_passages.docid: 913
negative_passages.text: Evaluating $\sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}$