Induction: $2^n = \sum_{v=0}^{n} \binom{n}{v}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
1167
How to prove that $\sum_{k=0}^{n}(-1)^k \binom {n}{k}=0 $
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
107810
Induction with Binomial Coefficients
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.
86896
Prove by induction. How do I prove $\sum\limits_{i=0}^n2^i=2^{n+1}-1$ with induction?
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
10777
Proof of the identity $2^n = \sum\limits_{k=0}^n 2^{-k} \binom{n+k}{k}$
153123
Proving by induction $4^n  0$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
65315
Showing $1+2+\cdots+n=\frac{n(n+1)}{2}$ by induction (stuck on inductive step)
108318
counting proof for $\sum_{k=0}^{n-1} 2^{k} = 2^n - 1$