New posts in Binomial Coefficients

How to prove an identity by induction

A power series equality involving binomial coefficients

A sum involving a binomial

Is this identity trivial? $n^n=n!+\sum_{k=1}^{n-1}(-1)^{k+1}\binom{n}{k}(n-k)^n$

Can I get a light hint for this binomial proof?

Evaluating a triple summation ${\sum \sum \sum}_{1 \le i < j \le k \le 20} a_ia_ja_k$

A Combinatorial/Algebraic Solution to Combinatorics Identities Exercise

If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$

Looking for a proof of two combinatorial summation identities

Can this be proved using Combinatorics or generating functions?