sequences and series - Evaluate $1+left(frac{1+frac12}{2}right)^2+left(frac{1+frac12+frac13}{3}right)^2+left(frac{1+frac12+frac13+frac14}{4}right)^2+...$

Evaluate:

$$S_n=1+\left(\frac{1+\frac12}{2}\right)^2+\left(\frac{1+\frac12+\frac13}{3}\right)^2+\left(\frac{1+\frac12+\frac13+\frac14}{4}\right)^2+...$$

a_n are the individual terms to be summed.

My Try :

$$\begin{align} &a_1=1\\ &a_2=\left(\frac{3}{4}\right)^2=\frac{9}{16}\\ &a_3=\left(\frac{11}{18}\right)^2\\ &a_4=\left(\frac{25}{48}\right)^2 \end{align}$$
now :?