query: An interesting combinatorial identity
positive_passages.docid: 29828
positive_passages.text: Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
negative_passages.docid: 74924
negative_passages.text: identity element of $(D_n ,\gcd)$
negative_passages.docid: 65983
negative_passages.text: Combinatorial proof of binomial coefficient summation identity
negative_passages.docid: 156383
negative_passages.text: Proving a combinatorial identity without double counting
negative_passages.docid: 36388
negative_passages.text: How to derive this Combinatorial identity
negative_passages.docid: 34299
negative_passages.text: Combinatorial proof of $\sum_{k=0}^n k \cdot k! = (n+1)! -1$
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.
negative_passages.docid: 42062
negative_passages.text: Interpretation of a combinatorial expression
negative_passages.docid: 76635
negative_passages.text: Proof through combinatorial argument
negative_passages.docid: 33104
negative_passages.text: Combinatorial Proof with Summation Identity
negative_passages.docid: 125174
negative_passages.text: Combinatorial intuition of identity
negative_passages.docid: 34386
negative_passages.text: Sum of a complex, finite geometric series and its identity
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: 27585
negative_passages.text: Combinatorial proof of Stirling Number Identity (First Kind)
negative_passages.docid: 146810
negative_passages.text: How to derive this binomial identity?
negative_passages.docid: 27141
negative_passages.text: Combinatorics identity question
negative_passages.docid: 15666
negative_passages.text: explanation for a combinatorial identity involving the binomial coefficient