query: How can I prove this Formula (about sum of r-combination of multiset)?
positive_passages.docid: 8476
positive_passages.text: Proof of the Hockey-Stick Identity: $\sum\limits_{t=0}^n \binom tk = \binom{n+1}{k+1}$
negative_passages.docid: 104411
negative_passages.text: sum of two connected subset of $\mathbb{R}$
negative_passages.docid: 70827
negative_passages.text: Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
negative_passages.docid: 56370
negative_passages.text: Associative operation on a set $S$
negative_passages.docid: 10976
negative_passages.text: Using induction to prove that $\sum_{r=1}^n r\cdot r! =(n+1)! -1$
negative_passages.docid: 19776
negative_passages.text: Simplify a combinatorial sum
negative_passages.docid: 1139
negative_passages.text: Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
negative_passages.docid: 57986
negative_passages.text: Sum of products of combinatorials
negative_passages.docid: 26790
negative_passages.text: Proving the geometric sum formula by induction
negative_passages.docid: 111032
negative_passages.text: Proof of Sets involving the Cartesian Product
negative_passages.docid: 23764
negative_passages.text: Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
negative_passages.docid: 7785
negative_passages.text: Cardinality of sum-set
negative_passages.docid: 90904
negative_passages.text: Combinatorial proof of an identity with squared binomial coefficients
negative_passages.docid: 345
negative_passages.text: Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.
negative_passages.docid: 143945
negative_passages.text: Summation of combination of binomial coefficient
negative_passages.docid: 9046
negative_passages.text: Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$
negative_passages.docid: 47670
negative_passages.text: Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$