There is a plan to follow for each proof by induction, and you don't have to think much to advance quite a bit. If you don't have anything better, you can find one description here. Or explain what exactly you don't understand. See also rule #11 in this sticky thread.
Ok, i understand. I am sorry, actually these are from my homework (the easier ones), but have no idea how to start. Maybe at a. I should prove for P(1), then for P(n+1)? Then it will be 1*2+2*3+...+(n+1)(n+2) ?
For b. I have no idea what should I do