Sum of series $S$ = $\frac{1}{2}$+$\frac{1}{3}\;(1+2)$+$\frac{1}{4}\;(1+2+3)$+$\frac{1}{5}\;(1+2+3+4)$+......upto 20 terms is

Question

$(a)\;110\qquad(b)\;105\qquad(c)\;115\qquad(d)\;116$