Find generating function of given problem?

Question

please help me to find the generating function of this problem
$a_k = ( k + 1) for  k=0,1,2,3,...$

Answer 1

$$f(x)=\sum_{k\ge 0}(k+1)x^k=\left(\sum_{k\ge 0}x^k\right)'=\left(\frac{1}{1-x}\right)'= {\rm etc}.$$