Hello, Sabo!

First, we must find the formula . . .What is the sum of: . ?

Prove the assumption by means of induction.

We have: .

If you are familiar with "Partial Fractions", this should be familiar.

We will rearrange the function into two fractions:

. .

Multiply by

. . Let

. . Let

Hence: .

We have: .

Note that most of the fractions cancel out.

. . And we are left with: .

Therefore: .

Andis the assumption that we must prove by Induction.that