Answer:
It depends. (Don't you just hate it when the answer begins like that?)
A set like that can come to a finite limit, or become infinite.
For example,
1 + x/1! + x2/2! + x3/3! + ... where n! denotes 1*2*3*...*n converges to e, the irrational number that is the base of natural logarithms. e = 2.71828 (approx).
Or
4/1 - 4/3 + 4/5 - 4/7 + ... = π, the irrational number which is the ratio of the circumference of a circle to its diameter.
Or
1 + 1/2 + 1/4 + 1/8 + 1/16 + ... which converges to 2.
On the other hand,
1 + 1/2 + 1/3 + 1/4 + 1/5 + ... keeps growing - forever.