Combinatory Explanation for $ \sum_{k=1}^{100} {{100} \choose {k}}2^k=3^{100}-1 $
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
116461
Prove the identity $\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}=0$ using a combinatorial interpretation of the positive and negative terms
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
142666
Algebric proof for the identity $n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
84010
Combinatorial proof that $\sum \limits_{k=0}^n \binom{2k}{k} \binom{2n-2k}{n-k} (-1)^k = 2^n \binom{n}{n/2}$ when $n$ is even
143113
Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$
107397
Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
36388
How to derive this Combinatorial identity
44484
Combinatorial identity $i{n \choose i } =n {n-1 \choose i - 1}$
132081
Geometrical interpretation of $(\sum_{k=1}^n k)^2=\sum_{k=1}^n k^3$
67927
Combinatorial argument for the identity $k\binom{n}{k} = n\binom{n-1}{k-1}$