Without using the proof by induction establish the formula for the simple arithmetic series
65648
Different ways to come up with $1+2+3+\cdots +n=\frac{n(n+1)}{2}$
17491
Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$
12487
Prove derangement formula by induction
115435
Induction: prove using congruences
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
11407
Proving the summation formula using induction: $\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$
155897
Proof by induction - is this correct?
82069
How to explain the formula for the sum of a geometric series without calculus?
35168
How to use combinatorial proof instead of induction?
124917
Fibonacci numbers and proof by induction
115912
Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
13297
Prove the following trigonometric identity without a calculator involved
15100
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
136700
Proving divisibility of expression using induction
133331
Proof by induction: $\sum\limits_{i=1}^{n} \frac{1}{n+i} = \sum\limits_{i=1}^{n} \left(\frac{1}{2i-1} - \frac{1}{2i}\right)$
68308
A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$