Have learned about induction a few weeks ago and found it both very useful but also unreliable. Because you need to have a good idea about what the term you're actually looking for is and it just confirm your guess. Anyway I had an idea and wanted to see how I develop it I was trying to find a closed form for the sum from i=one to n of i^k (sum of squares, cubes etc ...) I decided to call this f(k) (and I'll also call this g(n) you'll see shortly why) and then the sum again but up until n 1 is equal to f(k) (n 1)^k and I call this expression g(n 1). My target is to find the closed from of f(k), is there some way I can do it? Am I on the right path?