Sum of $n$ terms of series $S$ = $1$ + $2 \;(1+\frac{1}{n})$ + $3(1+\frac{1}{n})^2$ + ....is given by

Question

$(a)\;(n+1)^2\qquad(b)\;n(n+1)\qquad(c)\;n^2\qquad(d)\;\frac{n(n+1)}{2}$