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 :?