Question

What is a convergent series? what is a divergent series?.

Answer 1

Explanation:

A convergent series is a series whose partial sums tend to a specific number or a limit.

Example:
`3+1+(1)/(3)+(1)/(9)+.~.~.`

This is because a series is convergent if

`-1 < r < 1`

where r is the common ratio

and for the question above

`r=(1)/(3)`

A divergent series is a series whose partial sums do not approach a limit. Divergent series typically go to positive infinity, negative infinity, or don't approach a specific number.

Example:
`4+12+36+108~.~.~...`

This is a divergent series because the common ratio is;

`r=(12)/(4) =3`

Hope this helps! =)

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