query: Evaluating $\sum_{k=1}^{n} 2^{k}k$
positive_passages.docid: 6416
positive_passages.text: How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
negative_passages.docid: 108318
negative_passages.text: counting proof for $\sum_{k=0}^{n-1} 2^{k} = 2^n - 1$
negative_passages.docid: 131023
negative_passages.text: Evaluate the sum: $\sum\limits_{n=0}^{\infty} \frac1{F_{(2^n)}}$
negative_passages.docid: 92784
negative_passages.text: Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
negative_passages.docid: 136444
negative_passages.text: Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
negative_passages.docid: 151477
negative_passages.text: computing the series $\sum_{n=1}^\infty \frac{1}{n^2 2^n}$
negative_passages.docid: 71797
negative_passages.text: Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
negative_passages.docid: 146651
negative_passages.text: Evaluting sum $\sum \limits_{n=0}^\infty\frac{n^k}{n!}$
negative_passages.docid: 64581
negative_passages.text: How to find the sum $\sum\limits_{k=1}^n (k^2+k+1)k!$?
negative_passages.docid: 126105
negative_passages.text: Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
negative_passages.docid: 43509
negative_passages.text: Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$
negative_passages.docid: 19868
negative_passages.text: Evaluate: $ \sum _ {k=1}^{n}{\frac{k}{n}\binom{n}{k}t^k(1-t)^{n-k}}$
negative_passages.docid: 87589
negative_passages.text: Evaluate $\binom{n}{0}+\binom{n}{2}+\binom{n}{4}+...+\binom{n}{2k}$
negative_passages.docid: 104704
negative_passages.text: Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
negative_passages.docid: 6838
negative_passages.text: Evaluate the series $S_n = \sum_{k=1}^n\log\frac {k (k + 2)}{(k + 1)^2}$
negative_passages.docid: 116723
negative_passages.text: Evaluating the sum $\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$
negative_passages.docid: 151179
negative_passages.text: Finding the value of $\sum k/3^k$