Q.Let $S_n = 1 + \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{n}$. If $S_n = \dfrac{n}{n+1} S_{n-1} + \dfrac{1}{n(n+1)}$ for all $n \ge 2$ and $S_1 = 1$, then $S_{100}$ equals