prove by induction that $\sum_{k=0}^n {n \choose k} = 2^n$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
6165
Proof by Induction $n^2+n$ is even
123427
Proving the sum of the first $n$ natural numbers by induction
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
123955
How to compute $\sum\limits_{k=0}^n (-1)^k{2n-k\choose k}$?
141446
Proving by induction that $\sum\limits_{k=2}^n \frac1{k^2}\le 1$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
50226
Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
67886
How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
18046
Prove the following equality: $\sum_{k=0}^n\binom {n-k }{k} = F_n$
1167
How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
68080
Evaluation of $\sum_{k=0}^n{n\choose k}^2u^k$
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction