Probability and Moment Generating Functions

Hello,

I am terrible when it comes to probability and moment generating functions. I missed 2 lectures this week and I am now completely lost on the topic.I have two questions that I need to do by tomorrow and I was hoping if shown how to do one of the questions, I could work out the other one myself as it is similar.

Here is the first question:

Let Xn be a discrete random variable that takes the values 1,2,...,n with equal probability 1/n. Find the probability generating function of Xn and then determine its moment generating function. Determine the moment generating function of Yn = Xn/n. Show that the moment generating function of Yn = Xn/n converges pointwise to the moment generating function of a random variable that is uniformly distributed on (0,1).

I know this is a lot to do, so even if someone could tell me what it is I have to do here would be great. Like I said, I missed 2 lectures so Ive tried to learn this concept on my own, and have had nobody to correct any assumptions I make that are incorrect. Thank-you.