Using Binomial Theorem for proofs.
7083
Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
5801
Combinatorial proof help
67650
Short and intuitive proof that $\left(\frac{n}{k}\right)^k \leq \binom{n}{k}$
126587
Divisiblity of binomial coefficients
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
152084
Binomial-Theorem proof
71564
Combinatorial proof of identity involving central binomial coefficients
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
141814
Proofs using theorems instead of axioms
142589
Prove inequality of binomial theorem $\frac1{n^i}\binom{n}i \leq\frac1{m^i}\binom{m}i $.
18301
Proof by Induction involving Inequality and Factorials as denominators
124917
Fibonacci numbers and proof by induction
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
52557
Derivation of binomial coefficient in binomial theorem.
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
63510
Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
56317
Intuitive explanation of binomial coefficient formula