Question

Write an example of an infinite geometric series in which |r| > 1. Why does this type of series not converge?

Answer 1

it is G.S.
For r>0
take 10,100,1000,.......................as example
the series is increasing and tends to infinity so
it is not bounded
if it is not bounded, it has no limit.

for r<0
take -10,-100,-1000,.............. as example
the series is decreasing which is similiar to the case for r>0

For a convergent series,
there are two cases:
First,

the series is increasing and bounded above

Second,

the series is decreasing and bounded below

Answer 2

so what could the example be?

Answer 3

@CoCoTsoi