You should take the sum of I.H (k^2) and substitute that in for 1 + 3 + 5 + … (2k - 1) since we are assuming they equal each other. So you can now do, k^2 + 2k + 1 = (k + 1)^2.
Thanks for the course, but this should be seen according to the roden of the youtube playlist or according to the number of the videos "5.1.1, 5.1.2......"?