Use the moment-generating function to find the mean

I have the moment-generating function for the discrete uniform distribution \(f(x)=\frac{1}{k}\) for x=1,2,...k:


I need to take the derivative of this function with respect to t then find the limit as t approaches 0. I've tried L'Hospital's Rule for this limit with no luck. Any suggestions?


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Are you sure you have the correct mgf? To me it looks very close but there is a slight difference from what I would expect.
I made a mistake. It should be \(Mx(t)=\frac{e^t(1-e^{kt})}{k(1-e^t)}\). Although, I think I run into the same problem.
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\(\lim_{t\to 0}Mx'(t)= \mu\) However, this is of the form 0/0. If I use L'Hospital's rule, I will continue to get 0/0. Any suggestions?

What is the use of this mgf if it isn't helpful?