Question

How do you differentiate between convergent and divergent geometric series?

Answer 1

You need to look at the common ratio, r. If:\[|r|< 1\]its convergent. If not, its divergent.

Answer 2

Is that absolute value of r?

Answer 3

yes.

Answer 4

So in order for it to be concergent r has to be a fraction/decimal.

Answer 5

convergent*

Answer 6

One thats absolute value is less than one. \[r=\frac{5}{4}\]would make a divergent series.

Answer 7

While:\[r=\frac{4}{5}\]would make a convergent one.

Answer 8

Ok, that makes sense. Thanks