query: Evaluate $\sum\limits_{k=3}^{k=7} {(k+1)\choose (7-k)}$
positive_passages.docid: 26973
positive_passages.text: Relation between Pascal's triangle and fibonacci series.
negative_passages.docid: 90519
negative_passages.text: Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$
negative_passages.docid: 50606
negative_passages.text: Find $\sum\limits_{k\, \text{ odd}} \frac{2(k^2-1)}{k^4+k^2+1}$
negative_passages.docid: 13098
negative_passages.text: Find a formula for $\sum\limits_{k=1}^n \lfloor \sqrt{k} \rfloor$
negative_passages.docid: 634
negative_passages.text: Closed form formula for $\sum\limits_{k=1}^n k^k$
negative_passages.docid: 84595
negative_passages.text: How to evaluate $\lim\limits_{n\to+\infty} \prod\limits_{k=1}^n (1+k/n^2)$?
negative_passages.docid: 14399
negative_passages.text: Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
negative_passages.docid: 155382
negative_passages.text: Find $ \lim\limits_{{n \to \infty}} \frac1{2^n} \sum\limits_{k=1}^n \frac1{\sqrt{k}} \binom nk$
negative_passages.docid: 123675
negative_passages.text: Evaluate the following limit of finite sum
negative_passages.docid: 69309
negative_passages.text: How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$?
negative_passages.docid: 68080
negative_passages.text: Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
negative_passages.docid: 146651
negative_passages.text: Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$
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: 20317
negative_passages.text: Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
negative_passages.docid: 114280
negative_passages.text: Computing $\sum_{n=1}^∞\frac{1}{(n+1)(n+2)(n+3)....(n+p)}$
negative_passages.docid: 115420
negative_passages.text: Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$
negative_passages.docid: 91933
negative_passages.text: Evaluate $\sum_{k=1}^nk\cdot k!$