query: Prove by induction of binomial coefficients
positive_passages.docid: 30136
positive_passages.text: Proof that a Combination is an integer
negative_passages.docid: 31196
negative_passages.text: Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
negative_passages.docid: 126312
negative_passages.text: How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
negative_passages.docid: 52557
negative_passages.text: Derivation of binomial coefficient in binomial theorem.
negative_passages.docid: 105237
negative_passages.text: Alternating sum of binomial coefficients identity
negative_passages.docid: 16347
negative_passages.text: Induction: $\sum_{k=0}^n \binom nk k^2 = n(1+n)2^{n-2}$
negative_passages.docid: 144571
negative_passages.text: A conjecture including binomial coefficients
negative_passages.docid: 72026
negative_passages.text: Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
negative_passages.docid: 134202
negative_passages.text: Proof by Induction - Math
negative_passages.docid: 6803
negative_passages.text: Expression for power of a natural number in terms of binomial coefficients
negative_passages.docid: 29828
negative_passages.text: Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
negative_passages.docid: 96903
negative_passages.text: How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
negative_passages.docid: 67844
negative_passages.text: Prove equation with binomial coefficient
negative_passages.docid: 112827
negative_passages.text: Find the sum of the binomial coefficients
negative_passages.docid: 130093
negative_passages.text: Prove by Induction : $n < 2^n$
negative_passages.docid: 108401
negative_passages.text: Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
negative_passages.docid: 96673
negative_passages.text: Prove central binomial coefficient upper bound