Use the Ratio Test to find the interval of convergence of SUM [(-3x)^n/3n+1 ]. I have -1/3

Question

Use the Ratio Test to find the interval of convergence of SUM [(-3x)^n/3n+1 ]. I have -1/3<x<1/3.  The trouble is how to plug it into the equation and if it converges & stuff.

zarkon · Answer

your interval is a little off

anonymous · Answer

What did you get??

zarkon · Answer

$$\left(-\frac{1}{3},\frac{1}{3}\right]$$

zarkon · Answer

$$-1/3<x\le 1/3$$

anonymous · Answer

Ok ,s o how do you know that 1/3 is included??

zarkon · Answer

alternating series test

anonymous · Answer

Wellllll........i did the AST to get those two answers. But should I plug those into the equation?

zarkon · Answer

you need to plug -1/3 and 1/3 into the orignial sum for x and then test for convergence

anonymous · Answer

oooooooooooh, im sorry. I understand. What I did was called the Ratio test. But now I need to use the AST.

zarkon · Answer

you need to check the end points...with one of them (1/3) you can use the ast