you've almost come to the end. All you have to do is simplify the final expression (where you said you are stuck) which eventually gives you
Use mathematical induction to prove that each proposition is valid for all positive integral values of n
1^2+3^2+5^2+...+(2n-1)^2=n(2n-1)(2n+1)/3 This is what I did
(2k+1)^2
k(2k-1)(2k+1)/3
k(2k-1)(2k+1)/3 + (2k+1)^2/1
k(2k-1)(2k+1)/3 + 3(2k+1)^2/3
k(2k-1)(2k+1)/3 + 3(2k+1)(2k+1)/3 Now I am kind of stuck
Basically what I need is a formula that when n=k+1 is applied to n(2n-1)(2n+1)/3
it will give me the same result but I need to prove it.