Use the ratio test,

lim |q|^{n+1}/|q|^n=|q|<1

Thus,

The infinite series,

SUM |q|^n---->Converges.

But then the sequence must converge to zero,

That it,

lim |q|^n---->0

----

b)

If |q|>1

Then multiplication by |q|>0 yields,

|q|^2>|q|

Again,

|q|^3>|q|^2

Again and again...

Thus the sequence is not bounded.