query: Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
positive_passages.docid: 14306
positive_passages.text: What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$
negative_passages.docid: 76296
negative_passages.text: Compute $\frac{1}{e}\sum\limits_{n=0}^{\infty}\frac{n^{k}}{n!}$ for $k=0, 1, 2 ... $
negative_passages.docid: 148949
negative_passages.text: Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
negative_passages.docid: 9610
negative_passages.text: Find the sum of $\sum\limits_{n=1}^{\infty} \frac{x^{n}}{n(n+1)}$
negative_passages.docid: 9046
negative_passages.text: Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$
negative_passages.docid: 5332
negative_passages.text: Find the value of $\sum_0^n \binom{n}{k} (-1)^k \frac{1}{k+1}$
negative_passages.docid: 99420
negative_passages.text: Compute $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$
negative_passages.docid: 74294
negative_passages.text: How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
negative_passages.docid: 129734
negative_passages.text: Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
negative_passages.docid: 139074
negative_passages.text: Question about $a_n=\sum_{k=1}^n \frac{n}{n^2+k}\ $for $ n \in\mathbb{N}$
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: 3798
negative_passages.text: Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
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: 50972
negative_passages.text: Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
negative_passages.docid: 43903
negative_passages.text: Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
negative_passages.docid: 11407
negative_passages.text: Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
negative_passages.docid: 91784
negative_passages.text: Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$