# Math Help - Prove that a series is convergent

1. ## Prove that a series is convergent

ps; Zn = Z sub n

suppose that { Z n } is a sequence satisfying Re Zn >=0, and that the two series
1) sumation from (1 to infinity ) of Zn
and
2) sumation from (1 to infinity ) of |(Z^2n )| ---- where Z^2n is z power 2, then sub n
are convergent series.
prove that the series sumation from (1 to infinuty ) of (l Zn l )^2 is also convrgent

any idea? really ...i started by saying that
zn = xn +iyn
summation of zn is convergent, then summation of (xn +iyn) is also convergent.... but then i got stuck...plz help

2. It was already discussed here.