Prove $\sum^n_{k=0}{n \choose k} 2^k=3^n$
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
36639
Prove by induction that $\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$
1167
How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
142132
How do you prove $\sum \frac {n}{2^n} = 2$?
125297
Induction to prove $2n + 3 < 2^n$
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
67527
Proof by Induction that $3^n ≥ 1+2^n$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
345
Proving $ \sum _{k=0} ^m \binom nk \binom{n-k}{m-k} = 2^m \binom {n}{m}$.
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
103504
Weird $3^n$ in an identity to be combinatorially proved
20317
Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$