Question

interval of convergence of...
(-1)^n*(x+2)^n / n^2, n goes from 0 to infinity.
I know you use the ratio test but how do you get rid of the x before you take the limit??

Answer 1

i need help im really bad at math and i still cant figure out slope intercept form can you help me on this problem:
i have to write an equation in slope intercept form that passes through the given points.
2,-2 , (5,7)

Answer 2

You don't. You take the limit and treat the x as a constant.

Answer 3

Then you get (whatever after limit)<|1| Then you use that to solve for the radius.

Answer 4

Errr...|whatever after limit|<1** (what it should read)

Answer 5

What did you get for the ration n+1/n? (before you take the limit)

Answer 6

lim of -n^2/(n+1)^2 *(x+2)

Answer 7

Yes. Or written as:
\[\lim_{n \rightarrow \infty} |(\frac{n}{n+1})^2 (x+2)|<1\].
Since you take the abs value you can ignore the -.So taking the limit you can divide the ()^2 by n.
\[\lim_{n \rightarrow \infty} |(\frac{1}{1+\frac{1}{n}})^2 (x+2)|<1\].
That limit gives you |x+2|<1
Or:
-1<x+2<1
-3<x<-1.

Answer 8

Tell me if you need elaboration :P

Answer 9

got it! thanks!

Answer 10

No problem :D

Answer 11

Then, you need to plug in the endpoints in for x. See if the series converges, if it DOES then it has a closed interval for that x value. If the series DIVERGES, then its open.
For example: if -3 made the series converge, and the -1 made it diverge. You would have: [-3,-1) (I'm not sure which one either does xP)

Answer 12

oo rite..always forget that step! thanks again

Answer 13

Haha, no problem :P

Answer 14

wat does the radius of convergence mean?

Answer 15

So you have -3 to -1 they are 2 units apart right? In other words -1-(-3)=2 The radius is half of the interval, or 1.