Prove that $\binom{n+1}k = \binom nk + \binom n {k-1}$
424
Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$
64378
Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
74887
Combinatorial proof of the identity ${n+1\choose k+1}={k\choose k}+{k+1\choose k}+...+{n-1\choose k}+{n\choose k}$
4610
Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
120074
Prove by Combinatorial Argument that $\binom{n}{k}= \frac{n}{k} \binom{n-1}{k-1}$
152084
Binomial-Theorem proof
107021
Finding a combinatorial argument for an interesting identity: $\sum_k \binom nk \binom{m+k}n = \sum_i \binom ni \binom mi 2^i$
94580
Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
37569
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $