query: Proving that a binomial coefficient is the sum of two others
positive_passages.docid: 25004
positive_passages.text: Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
negative_passages.docid: 8806
negative_passages.text: Summation of binomial coefficients
negative_passages.docid: 143927
negative_passages.text: Binomial coefficients that are powers of 2
negative_passages.docid: 79124
negative_passages.text: Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$
negative_passages.docid: 52557
negative_passages.text: Derivation of binomial coefficient in binomial theorem.
negative_passages.docid: 154280
negative_passages.text: Show this equality (The factorial as an alternate sum with binomial coefficients).
negative_passages.docid: 35342
negative_passages.text: Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
negative_passages.docid: 91648
negative_passages.text: Binomial coefficient proof
negative_passages.docid: 126312
negative_passages.text: How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
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: 133181
negative_passages.text: Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
negative_passages.docid: 18046
negative_passages.text: Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
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: 92704
negative_passages.text: Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
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: 41354
negative_passages.text: Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
negative_passages.docid: 103347
negative_passages.text: combinatorial proof of summation