query: Compute Using Binomial Theorem
positive_passages.docid: 23557
positive_passages.text: Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
negative_passages.docid: 59638
negative_passages.text: How to prove this result on binomial coefficients?
negative_passages.docid: 71769
negative_passages.text: Evaluation of ratio of two binomial expression
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: 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: 47052
negative_passages.text: How can I simplify this expression involving binomial coefficients?
negative_passages.docid: 17638
negative_passages.text: Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
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: 157552
negative_passages.text: Find the coefficient of $x^n$ simply by using binomial theorem
negative_passages.docid: 11335
negative_passages.text: Proving Binomial Identity without calculus
negative_passages.docid: 112827
negative_passages.text: Find the sum of the binomial coefficients
negative_passages.docid: 49234
negative_passages.text: Sum of binomial coefficients with index divisible by 4
negative_passages.docid: 104704
negative_passages.text: Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
negative_passages.docid: 118674
negative_passages.text: Simple upper bound for $\binom{n}{k}$
negative_passages.docid: 101573
negative_passages.text: Subtracting even and odd binomial coefficients?
negative_passages.docid: 66019
negative_passages.text: Revisited: Binomial Theorem: An Inductive Proof
negative_passages.docid: 90293
negative_passages.text: How expand Binomial[n, k] for k >= 6?