Consider the following sum of a series:

s(n,X) = sum for i = 1 to n of 1/(n+nX+i-1)

Where, i and n are integers, and X is a free variable that may take any value >= 0.

For example, when n = 3, we have:
s(3,X) = 1/(3+3X) + 1/(3+3X+1) + 1/(3+3X+2)

I am trying to derive an analytical expression f(X) (not a summation) which gives the limit of the sum s(n,X) as n tends to infinity i.e. f(X) = s(infinity,X).

Suggestions as to an expression and proof would be most welcome.

Many thanks

Rob