The question asks to verify that each equation is true for every positive integer n.
The question is as follows:
$$1+ 3 + 5 + \cdots + (2n - 1) = n^2$$
I have solved the base step which is where $n = 1$.
However now once I proceed to the inductive step, I get a little lost on where to go next:
Assuming that k is true (k = n), solve for k+1: (2k - 1) + (2(k+1) - 1) (2k - 1) + (2k+2 - 1) (2k - 1) + (2k + 1)
This is where I am stuck. Do I factor these further to obtain a polynomial of some sort? Or am I missing something?