query: Binomial expansion of $(x_{1}+x_{2}+...........+x_{k})^{n} $
positive_passages.docid: 156395
positive_passages.text: how many terms will there be once you collect terms with equal monomials? What is the sum of all the coefficients?
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: 152588
negative_passages.text: Expression for $n+n(n-1)+n(n-1)(n-2)+...+n!$
negative_passages.docid: 112827
negative_passages.text: Find the sum of the binomial coefficients
negative_passages.docid: 27922
negative_passages.text: prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
negative_passages.docid: 14399
negative_passages.text: Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$
negative_passages.docid: 58972
negative_passages.text: Proof/Derivation of Closed form of Binomial Expression $\sum\limits_{k=0}^{2n}(-1)^k\binom{2n}{k}^2$
negative_passages.docid: 6803
negative_passages.text: Expression for power of a natural number in terms of binomial coefficients
negative_passages.docid: 158774
negative_passages.text: Series of binomial coefficients: $\sum\limits_{n=k}^{\infty}{\binom nk}x^n=\frac{x^k}{(1-x)^{k+1}}$
negative_passages.docid: 79814
negative_passages.text: Calculate sums of inverses of binomial coefficients
negative_passages.docid: 91239
negative_passages.text: Sum of binomial coefficients involving $n,p,q,r$
negative_passages.docid: 96945
negative_passages.text: General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
negative_passages.docid: 143264
negative_passages.text: Is there a nice way of expanding multinomials of the form $(1+x+\cdots+x^l)^n$?
negative_passages.docid: 105325
negative_passages.text: Expansion of $(1+px+qx^2)^8\equiv 1+8x+52x^2+kx^3$...
negative_passages.docid: 120074
negative_passages.text: Prove by Combinatorial Argument that $\binom{n}{k}= \frac{n}{k} \binom{n-1}{k-1}$
negative_passages.docid: 158508
negative_passages.text: Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
negative_passages.docid: 67927
negative_passages.text: Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$