Proof by Induction: Summation

Question

Hello. I am just beginning proof by induction. Would anyone be willing to see if I am grasping this correctly?

Answer 1

It's correct, but just with some typos. It should be $6(k+1)^2$ instead of $6+(k+1)$ on your third last line, and you missed a right bracket on your last line of proof. Also, usually it's easier to edit and look for us if you can type it in mathjax.