Question

The power series CnX^n diverges at x=7 and converges at x=-3. At x=-4, the series is...

(a) conditionally convergent
(b) absolutely convergent
(c) divergent
(d) cannot be determined

Answer 1

It's conditionally convergent.

Answer 2

i already have the answer i need to know how to do these problems step by step

Answer 3

and it cant be determined is the correct answer

Answer 4

anybody wana show me how to do it step by step?

Answer 5

I can create 3 different \(C_n's\) so that you have one that conditionally converges at -4, one that absolutely converges at -4 and one that diverges at -4...can you?

Answer 6

if you can do that then the obvious answer is (d)

Answer 7

can u please work out the problem so i know how to do these

Answer 8

You are right the answer should be d)
Here why if your series diverges at x=7 so it diverges for any x such that |x|>7
Nothing can be said for |x|<7

Answer 9

If your series converges at x=-3 then it converges at any x such that |x| <3
Nothing can be said for |x|>3.
So nothing can be said for 3 < |x| < 7 so nothing can be said for x=-4

Answer 10

that makes no sense to me.

Answer 11

sorry:/

Answer 12

Go back to your books and study this topic.

Answer 13

they dont say anything for this type of question

Answer 14

This is a basic fact about power series.

Answer 15

they don't mention the radius of convergence?

Answer 16

They do not have too.

Answer 17

they should

Answer 18

nobody has explained or used specific terms on how to solve these problems. yes i know what radius of convergence is.

Answer 19

The question is clear and nothing else should be added to obtain the solution. We are dealing with power series

Answer 20

thank you for ur help. goodnight.