I need help with Math Induction

Question

1 + 3 + 5 + ... + ( 2n - 1) = n^2, for every positive integer?

Answer 1

1. It is true for k=1
2. 1=1^2
3. Let's assume it is valid for first K elements:
4. 1+3+...+(2k-1) = k^2

Now let's proof that if you add the next element, you will get (k+1)^2

So, the first k-elements add up k^2

The next element we are adding is (2k-1) + 2 (next odd number)

So the total sum will be

k^2 + (2k+1) =(k+1)^2 That's it!