The problem given was that I had to evaluate $L_n(0)$ given the generating function for Laguerre polynomials is:
$g(x,t) = \sum_{n=0}^{\infty} L_n(x) t^n = \frac {e^{xt/(1-t)}}{1-t}$
I tried substituting x as zero but I'm not sure it's correct because it seems too easy. I ended up with:
$\sum_{n=0}^{\infty} L_n(0) t^n = \frac {e^{xt/(1-t)}}{1-t}= \frac {e^0}{1-t} =\frac {1}{1-t}$
Am I going the right path? If yes, where can I go from here? If no, what should I have done? Thank you in advance to anyone who would be able to help me understand this better!