Infinite series convergence value problem 
Is it possible to find the convergent value of the series:  $\sum\limits_{x=0}^{\infty}(x+3) \cdot a^x $ where $a$ is a constant less than 1?

I thought about expanding:
$\sum\limits_{x=0}^{\infty}(x+3) \cdot a^x =\sum\limits_{x=0}^{\infty}x \cdot a^x + 3 \sum\limits_{x=0}^{\infty} a^x$
and the second term is just $\cfrac{3}{1-a}$, but I don't know what to do with the first term.  Is there a general method to solve these types of problems?  I that there are many types of convergent tests but not sure about methods to actually find convergent value.  Thanks in advance.

Continuing your own thoughts(Hint):
$$(\frac{1}{1-x})' = (\sum_{n=0}^{\infty}x^n)' = \sum_{n=1}^{\infty}nx^{n-1} = \sum_{n=0}^{\infty}(n+1)x^n$$
