** Claim: **

* Proof. * If on the left we have and on the right we have . Thus, the formula is true for the case .

Assume then that the formula is true for some . So,

Thus, if the formula is true for then it is true for . Since we have established that it is true for , we have that is true for all

There is a typo. It is 1/k – 1/k(k+1) instead of 1/k – 1/(k+1).