Please answer this and show your work as to how you did it

1. (10 points) Indicate Whether the following statements are True or False. If the statement is false provide a counter example (think of geometric and pseries that contradicts the statement). If the statement is true give reasoning. (1 point for T/F and 1 point for explanation) a) If the sequence {an} converges to 1 and the sequence {(13.1)} converges to 2. then the sequence {(gfff} has to converge to 4. b) If limyoo an 7E 0. then 220:1 an diverges. c) If 0 an, then Enzo hn diverges. d) limn +0 dn > 1 e) limn co Cn is either