IMC 2013 — Keystage 3 (IWYMIC) — individual Question 13

Let $$S_n=\sum_{i=1}^n\frac1i+\sum_{j=1}^n\left(\sum_{i=j}^n\frac1i\right)^2.$$ Each successive bracket drops the first term of the preceding bracket. Find $S_{2013}$.