query: Find the value of sum (n/2^n)
positive_passages.docid: 144078
positive_passages.text: What does $\sum_{k=0}^\infty \frac{k}{2^k}$ converge to?
negative_passages.docid: 148442
negative_passages.text: Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
negative_passages.docid: 56365
negative_passages.text: Evaluate $\sum\limits_{k=1}^{n} \frac{k}{2^k}$
negative_passages.docid: 36361
negative_passages.text: How to calculate the summation $(\sum_{p = k}^{n} \binom{n}{p}) / 2^n$ quickly?
negative_passages.docid: 3798
negative_passages.text: Finding formula for sum $S_n = \sum_{i=1}^n i(i-1)$
negative_passages.docid: 136066
negative_passages.text: Find the sum $\sum _{n=1}^{\infty }\left(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n}\right)$
negative_passages.docid: 112827
negative_passages.text: Find the sum of the binomial coefficients
negative_passages.docid: 29170
negative_passages.text: Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$
negative_passages.docid: 25504
negative_passages.text: How to find sum of the infinite series $\sum_{n=1}^{\infty} \frac{1}{ n(2n+1)}$
negative_passages.docid: 89367
negative_passages.text: Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
negative_passages.docid: 72360
negative_passages.text: Find the value of $a^{2m}+a^m+{1\over a^m}+{1\over a^{2m}}$
negative_passages.docid: 148949
negative_passages.text: Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
negative_passages.docid: 17056
negative_passages.text: How to find answer to the sum of series $\sum_{n=1}^{\infty}\frac{n}{2^n} $
negative_passages.docid: 112950
negative_passages.text: Find the value of infinite series $\sum_{n=1}^{\infty} \tan^{-1}(2/n^2)$
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: 57549
negative_passages.text: Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
negative_passages.docid: 143501
negative_passages.text: Find all $n\in\mathbb N^+$ such that the sum of the digits of $5^n$ is equal to $2^n$.