Simple Induction Proof: $\sum_{i=1}^{n} = \frac{i(i+1)}{2}$
101899
Proof By Induction of a Sum
143113
Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$
133331
Proof by induction: $\sum\limits_{i=1}^{n} \frac{1}{n+i} = \sum\limits_{i=1}^{n} \left(\frac{1}{2i-1} - \frac{1}{2i}\right)$
4991
Proving by induction that $ \sum_{k=0}^n{n \choose k} = 2^n$
123427
Proving the sum of the first $n$ natural numbers by induction
11407
Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
123757
Proving a summation inequality with induction
16177
Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
115912
Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$
142132
How do you prove $\sum \frac {n}{2^n} = 2$?
62556
Prove $3|n(n+1)(n+2)$ by induction
5272
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
40348
Proving by mathematical induction: $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}>2(\sqrt{n+1}-1)$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
88292
Prove by induction that $\sum\limits_{i=1}^n \frac{1}{n+i} \leq \frac{3}{4}$
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
108596
Proof by induction for "sum-of"