# Is the following series #6-2+2/3-2/9+2/27-2/81# convergent or divergent?

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I have this so far:

#1/3(-1)^n# **or** #1/3(-1)^(n-1)# .

I'm not sure which one it is.

Also, is #a_i=6# ?

I have this so far:

**or**

I'm not sure which one it is.

Also, is

##### 1 Answer

Apr 5, 2018

Read below.

#### Explanation:

We see that a given term, other than the first one, is the term before times negative one third.

The ratio is therefore

A series is convergent if the absolute value of the ratio is less than 1.

This series is convergent.

Also, this series is in the form

This type of series is generally in the form:

Therefore, the formula for the

Also, the first term of the series is

Therefore,