`sum_(n=0)^oo (-1)^nx^n` Find all values of x for which the series converges. For these values of x write the sum of the series as a function of x.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`sum_(n=0)^oo(-1)^nx^n` 

`=sum_(n=0)^oo(-1x)^n`

It is a geometric series with common ratio`r=-x` ,so the series converges for `|r|<1`  

`|-x|<1`

`=>|x|<1`

`=>-1<x<1`

In this case, Sum of the series=`a/(1-r)`

`=1/(1-(-x))`

`=1/(1+x)`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial