Probability

A whole number X of pounds is placed in an envelope, where P[X=x] is given below. The quantity 2X is placed in a second envelope.

You are given at random one of the two envelopes and open it to reveal x pounds. You are given the option to swap for the contents of the other envelope.

You decide to swap if the expected amount in the other envelope is more than x.

For what values of x would you swap when
(i) P[X=x] = (2/3)(1/3)^k when x=2^k for some k=1,2,...?

(ii) P[X=x] = (1/3)(2/3)^k) when x=2^k for some k=1,2,...?

ans: (i) swap only if x=1 (ii) swap for any x could someone plz tell me how to get these answers?