4. (40 points) Let Si(n) = [kuk, S2(n) = fku k2 and S3(n) = [h_k3. In the reading assignment Reading-Perturbation-Method.pdf it has been shown how to calculate Si(n) and S2(n). Now, use the same perturbation method to derive the formula for S3(n). (Background Information: You would need the formula of Si(n) and S2(n), which we already know: Si(n) = n(n + 1)/2 and S2(n) = n(n + 1)(2n + 1)/6.)