Using Binomial Theorem to prove the following
7083
Alternating sum of binomial coefficients: given $n \in \mathbb N$, prove $\sum^n_{k=0}(-1)^k {n \choose k} = 0$
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
4855
How to show that this binomial sum satisfies the Fibonacci relation?
146533
Having problems proving $ \sum_{r=0}^{n}(r+1) \binom{n}{r} = (n+2)2^{n-1} $
81729
Combinatorial proof of $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!$, using inclusion-exclusion
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$
61270
Binomial Theorem Sum
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$
35956
Proof that a sum of Bernoulli rvs has Binomial distribution
11335
Proving Binomial Identity without calculus
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
144571
A conjecture including binomial coefficients
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$