Summation $\displaystyle\sum_{k=1}^{n} \;k \begin{bmatrix}1 +\frac{1}{n} \end{bmatrix}^{k-1}$ is equal to :

Question

( A ) $n(n+1)$
( B ) $n(n-1)$
( C ) $(n+1)^2$
( D ) $n^2$