query: Finding a closed form of following summation
positive_passages.docid: 31970
positive_passages.text: Alternating sum of squares of binomial coefficients
negative_passages.docid: 19633
negative_passages.text: Closed form for a pair of continued fractions
negative_passages.docid: 158616
negative_passages.text: A closed form for the sum $S = \frac {2}{3+1} + \frac {2^2}{3^2+1} + \cdots + \frac {2^{n+1}}{3^{2^n}+1}$ is ...
negative_passages.docid: 47753
negative_passages.text: Closed form of series with factorial-squared denominator?
negative_passages.docid: 146274
negative_passages.text: Fastest way to do this double summation?
negative_passages.docid: 148883
negative_passages.text: Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$
negative_passages.docid: 120633
negative_passages.text: How to find sum of this series $\sum_{0}^{\infty} \frac{(n!)^{2}x^{n}}{(2n)!}$
negative_passages.docid: 129801
negative_passages.text: Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
negative_passages.docid: 45862
negative_passages.text: Nested sum of binomial coefficient in closed form
negative_passages.docid: 113713
negative_passages.text: Closed formula for the sum of the following series
negative_passages.docid: 150355
negative_passages.text: Finding sum of binomial series
negative_passages.docid: 42736
negative_passages.text: Is there a closed form for $\sum_{k=0}^n \frac{x^k}{k!}$?
negative_passages.docid: 116723
negative_passages.text: Evaluating the sum $\sum_{n=1}^{\infty}\dfrac{(-1)^{n}}{n^{2}}$
negative_passages.docid: 19914
negative_passages.text: Closed form for $\sum_{n=0}^{\infty} \binom{n+k}{k} x^n$ (Negative Binomial Theorem)
negative_passages.docid: 59253
negative_passages.text: Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $
negative_passages.docid: 115433
negative_passages.text: Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$
negative_passages.docid: 130945
negative_passages.text: Summation using residues