query: Proof by calculation binomial coefficient
positive_passages.docid: 142589
positive_passages.text: Prove inequality of binomial theorem $\frac1{n^i}\binom{n}i \leq\frac1{m^i}\binom{m}i $.
negative_passages.docid: 140632
negative_passages.text: A problem on Binomial Theorem
negative_passages.docid: 107071
negative_passages.text: Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
negative_passages.docid: 128913
negative_passages.text: A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
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: 79814
negative_passages.text: Calculate sums of inverses of binomial coefficients
negative_passages.docid: 133905
negative_passages.text: Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
negative_passages.docid: 4610
negative_passages.text: Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$
negative_passages.docid: 47052
negative_passages.text: How can I simplify this expression involving binomial coefficients?
negative_passages.docid: 150438
negative_passages.text: Binomial theorem for non integers ? O_o ??
negative_passages.docid: 113321
negative_passages.text: Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$
negative_passages.docid: 87505
negative_passages.text: binomial coefficient equal to sum
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: 52557
negative_passages.text: Derivation of binomial coefficient in binomial theorem.
negative_passages.docid: 143927
negative_passages.text: Binomial coefficients that are powers of 2
negative_passages.docid: 146200
negative_passages.text: proof by induction: sum of binomial coefficients $\sum_{k=0}^n (^n_k) = 2^n$
negative_passages.docid: 140607
negative_passages.text: Squared binomial coefficient