Thread: Analysis - complex sequences problem?

If you let {a_n} be a complex sequence where
lim [ |a_n|^(1/n) ] = q
i.e. the nth root of the modulus of the terms in the sequence tends to q.

(i) show that if q<1, then lim a_n=0
(ii) show that if q>1, then |a_n| --> infinity
iii) what can you say about the behaviour of |a_n| if q=1?

please help!

If is a real sequence and then converges to zero if .

So given a complex sequence we can write thus .
So,
.

Similarly .