Question

Determine if the series 12/5+48/25+192/125 is convergent or divergent​

Answer 1

The given series is convergent.

Explanation:

A series is called convergent when it has finite limit.

A series is called divergent when it has infinite limit.

To check the limit we have to use following methods ,

If | s | < 1 , the series is convergent , where s is the common ratio.

If | s | > 1 , the series is divergent.

⇒ s =
`(192)/(125) * (5)/(12) = (2)/(5) < 1`

⇒ s =
`(48)/(125) * (5)/(12) = (4)/(5) < 1`

∴ The given series is convergent.