I guess you mean "series", the sum of the terms of the sequence,

and you want to know if this sum converges as n goes to infinity.

So your should be

This is a geometric series, 1st term 1 and common ratio 0.5

Hence it's sum for n terms is

and as n goes to infinity, the numerator goes to 1, while the denominator is 0.5.

So the sum converges.