query: Finding $\binom n0+\binom n3+\binom n6+\cdots $
positive_passages.docid: 155496
positive_passages.text: sum of combinations $\binom n{0} + \binom n{3} + \binom n{6} +... +\binom n{3k}$
negative_passages.docid: 114277
negative_passages.text: Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
negative_passages.docid: 106441
negative_passages.text: Find the value of $\binom{2000}{2} + \binom{2000}{5} + \binom{2000}{8} + \cdots \binom{2000}{2000}$
negative_passages.docid: 106965
negative_passages.text: How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?
negative_passages.docid: 112827
negative_passages.text: Find the sum of the binomial coefficients
negative_passages.docid: 105237
negative_passages.text: Alternating sum of binomial coefficients identity
negative_passages.docid: 131326
negative_passages.text: How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
negative_passages.docid: 57549
negative_passages.text: Finding the sum $\sum_{k=1}^rk^2\binom {n-k}{r-k}$
negative_passages.docid: 482
negative_passages.text: Express $1 + \frac {1}{2} \binom{n}{1} + \frac {1}{3} \binom{n}{2} + \dotsb + \frac{1}{n + 1}\binom{n}{n}$ in a simplifed form
negative_passages.docid: 92704
negative_passages.text: Prove that $\sum_{k=1}^{n}k\binom{n}{k}=n\cdot2^{n-1}$
negative_passages.docid: 148949
negative_passages.text: Find the value of $\sum_{k=1}^{n} k \binom {n} {k}$
negative_passages.docid: 46132
negative_passages.text: Combinatorial interpretation for the identity $\sum\limits_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}$?
negative_passages.docid: 142994
negative_passages.text: How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?
negative_passages.docid: 122891
negative_passages.text: integer as sum of three binomials
negative_passages.docid: 126214
negative_passages.text: Multiplying Binomial Terms
negative_passages.docid: 142303
negative_passages.text: Alternating sum of binomial coefficients multiplied by (1/k+1)
negative_passages.docid: 111779
negative_passages.text: Ordinary generating function for $\binom{3n}{n}$