Prove $\sum_{k=0}^l \binom{n}{k}\binom{m}{l-k} = \binom{n+m}{l}$
52470
Spivak's Calculus - Exercise 4.a of 2nd chapter
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
87479
Closed form for $\sum_{k=0}^{n-p}\binom{n}{k}\binom{n}{p+k}$
143337
How to prove that $\sum_{i=0}^n 2^i\binom{2n-i}{n} = 4^n$.
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
35342
Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
49771
Prove that $\sum\limits_{k=0}^r\binom{n+k}k=\binom{n+r+1}r$ using combinatoric arguments.
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
64803
Counting two ways, $\sum \binom{n}{k} \binom{m}{n-k} = \binom{n+m}{n}$
155769
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n-1}$ using the binomial theorem for $n\geq1$
89576
Proof of a binomial identity $\sum_{k=0}^n {n \choose k}^{\!2} = {2n \choose n}.$
145048
Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
94784
$\sum_{k=-m}^{n} \binom{m+k}{r} \binom{n-k}{s} =\binom{m+n+1}{r+s+1}$ using Counting argument
46840
How to prove that $\sum_{r=0}^n\binom{n}{r}2^r=3^n$