The denominators in the given sequence can be expressed in powers of 4:
40, 42, 41 but the numerators are out of sequence. So assuming that the terms are placed in order and continuing the sequence, we have:
(X-2)/40, (X-2)2/41, (X-2)3/42, (X-2)4/43, (X-2)5/44, ..., (X-2)n+1/4n, ...
This is a geometric progression with common ratio r=(X-2)/4, a=(X-2)/40.
The sum of a GP is Sn (sum to nth term) and is given by:
Sn=a(1-rn)/(1-r). When n→∞, rn→0 if the series converges, that is, S∞=a/(1-r)→k where k is a fixed constant. So (X-2)n/4n→0. If X-2<4, then we have a series of fractions each of which is less than 1 and is decreasing. So X<6. For example, if X=5 then r=(X-2)/4=¾. S∞=¾/¼=3.