The correct option is C (x < -2) U (x > 2)
Common ratio (r) = 2x
For the sum of an infinite G. P. to be a finite no. its common ratio should lie between (-1, 1)
So, −1<2x<1
⇒ 2x<1
⇒ 2x−1<0
or 2−xx<0
⇒ xϵ(−∞,0)∪(2,∞)
Similarly, 2x>−1
2x>1>0
=2+x2>0
⇒ −∞,−2)∪(2,∞)
On taking intersection we get,
−∞,−2)∪(2,∞)