query: Vandermonde's Identity: How to find a closed formula for the given summation
positive_passages.docid: 42763
positive_passages.text: How to prove Vandermonde's Identity: $\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}$?
negative_passages.docid: 139307
negative_passages.text: Closed form expression for infinite series
negative_passages.docid: 55061
negative_passages.text: Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
negative_passages.docid: 47753
negative_passages.text: Closed form of series with factorial-squared denominator?
negative_passages.docid: 69084
negative_passages.text: What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
negative_passages.docid: 49960
negative_passages.text: Calculating Vandermonde determinant
negative_passages.docid: 129801
negative_passages.text: Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
negative_passages.docid: 92754
negative_passages.text: Closed form for the series: $\sum_{n=1}^{\infty}x^{n^2}$
negative_passages.docid: 113713
negative_passages.text: Closed formula for the sum of the following series
negative_passages.docid: 126236
negative_passages.text: General closed form of $\int_{0}^{\theta_0} \frac{1}{\sqrt{\cos \theta-\cos \theta_0}} d\theta$
negative_passages.docid: 127284
negative_passages.text: Closed form of $\int_0^{\pi/2} \frac{\arctan^2 (\sin^2 \theta)}{\sin^2 \theta}\,d\theta$
negative_passages.docid: 123507
negative_passages.text: How to find the closed form of multiplications of exponentials?
negative_passages.docid: 634
negative_passages.text: Closed form formula for $\sum\limits_{k=1}^n k^k$
negative_passages.docid: 23726
negative_passages.text: A closed form for $1^{2}-2^{2}+3^{2}-4^{2}+ \cdots + (-1)^{n-1}n^{2}$
negative_passages.docid: 30851
negative_passages.text: Find the summation $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \cdots$
negative_passages.docid: 155367
negative_passages.text: summation of multiplying series with negative terms
negative_passages.docid: 83346
negative_passages.text: Finding a closed form $x_n$ for the recurrence relation $x_{n+2} = px_{n+1} + qx_n + r$