Pre-Calc Proving Induction Problem

Hi, I need help with pre-calc - proofing induction

An : 1+3+5+...+(2n-1) = n^2

The proof is this:

An is true
An is true, An +1 is true
An is true for all n

I really don't understand how to prove this induction proof. Can anyone explain this to me? :)

To prove any induction proof, show that the theorem is true for n=1, then show that IF it's true for a value n, then it's also true for n+1:

A1: 1 = 1^2 - True

If sum (1 ... 2n-1) = n^2, then:

sum (1 ... 2n+1) = n^2 + 2n + 1 = (n+1)^2

QED.