# Proof rule

Hello I'm learning about proofs and in my book there's a sect. On mathematical induction. And I'm trying understand why this makes it true for all values.
1+3+5...2n-1=n^2
Suppose that the formula is known to be true for n=1, and suppose that as a result of assuming that it is true for n=k, where k is an arbitrary positive integer, we can prove that it is also true for n=k+1.
Then the formula is true for all k.

Why does this addition of 1 make it true for all k?