2010-09-14, 11:42 PM
You are on the right track. With induction you assume that the statement is true for k and show from that that the statement is true for k+1.
The induction hypothesis gives that SUM[(2r-1)^3] from r=1 to k is equal to k^2(2k^2-1). What you need to do is show that when you add (2(k+1)-1)^3 to the right side you get (k+1)^2(2(k+1)^2-1).
The induction hypothesis gives that SUM[(2r-1)^3] from r=1 to k is equal to k^2(2k^2-1). What you need to do is show that when you add (2(k+1)-1)^3 to the right side you get (k+1)^2(2(k+1)^2-1).