query: how can i prove this equation of binomial coefficients?
positive_passages.docid: 28737
positive_passages.text: Negative binomial coefficient
negative_passages.docid: 146200
negative_passages.text: proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
negative_passages.docid: 147910
negative_passages.text: Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
negative_passages.docid: 80155
negative_passages.text: Binomial coefficient problem
negative_passages.docid: 92704
negative_passages.text: Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
negative_passages.docid: 111951
negative_passages.text: Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
negative_passages.docid: 110441
negative_passages.text: Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?
negative_passages.docid: 10777
negative_passages.text: Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
negative_passages.docid: 10875
negative_passages.text: proof of binomial identity involving double sum
negative_passages.docid: 126888
negative_passages.text: How can you show that $\binom {n}{7}=\sum_{k=7}^n \binom {k-1} {6}$?
negative_passages.docid: 50226
negative_passages.text: Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
negative_passages.docid: 10917
negative_passages.text: Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
negative_passages.docid: 30338
negative_passages.text: How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
negative_passages.docid: 65983
negative_passages.text: Combinatorial proof of binomial coefficient summation identity
negative_passages.docid: 1158
negative_passages.text: How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
negative_passages.docid: 90904
negative_passages.text: Combinatorial proof of an identity with squared binomial coefficients
negative_passages.docid: 11612
negative_passages.text: How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?