First I considered the expansion of
(1 + x)<sup>n</sup> = <sup>n</sup>C<sub>0</sub> + <sup>n</sup>C<sub>1</sub>x + ... + <sup>n</sup>C<sub>n</sub>x<sup>n</sup>
I differentiated both side with respect to x, and got
n(1+x)<sup>n</sup> = <sup>n</sup>C<sub>1</sub> +...