Hello Christina,

it helps if you use the Sum notation:

The notation says that you add from k = 1 to n k. Anyway, it makes keeping track of the types of sums you're interested in easier. Example:

I'm not sure if that's the relation you're looking at, but in general, these kinds of induction work as follows. You chek the induction for a base case, such as n = 0;

That would actually be the end of the inductive proof unless you can find another base case, where the relationship is true. (Perhaps I didn't understand your question)

Then you accept as the hypothesis the relation and try and show that it's true for (n + 1) term. With sum notation it usually looks like this (I changed the starting point to k = 1):

You change the sum of n + 1 terms to:

substitue the hypothesis for the sum of the first n terms and show that if the assumption is true for n, it is also true for (n + 1):