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General form of a summation as a function of 2 variables

My goal is to have a general form of a summation that is a function of two variables, and would like to see if Mathematica can be used to determine the general form.

For example, with a single variable, is there a way to get Mathematica to take

sum_{k=0}^n (k/n)

and determine the general formula for the sum (as a function of 'n') is (n+1)/2?

The problem I am looking at is a bit more complicated (incorporates a five factorials) and is a function of two variables, m and n. I have never programmed in Mathematica (but do have programming experience in a few languages), and any direction on what resources or functions are appropriate for this sort of problem would be greatly appreciated. If this sort of thing can only be done in one variable, that would also be very useful since I'll just look at a particular case (when the two variables are equal: m=n).

Thanks much for any help,

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