Question

suppose that the power series CnX^n converges when x=-4 and diverges when x=7. Which of the following are true, false, or not possible to determine?

(a) x=10
(b) x=3
(c) x=1
(d) x=6

Answer 1

@agent0smith do u know?:)

Answer 2

@Hero do you know how to do this?

Answer 3

I assume you're asking if a, b, c and d converge/diverge.

Answer 4

yes

Answer 5

@Lessis

Answer 6

Have you seen convergence radii?

Answer 7

nope

Answer 8

http://en.wikipedia.org/wiki/Power_series could this help?

Answer 9

wait is power series the same thing as taylor series?

Answer 10

http://en.wikipedia.org/wiki/Radius_of_convergence

Answer 11

The series has a radius of convergence around 0, so any value of X that is in the radius of convergence, converges. You know that -4 is in the radius, so anything with a value smaller than |-4| converges. That means that B and C converge. Also, since 7 doesn't converge, anything higher than 7 doesn't converge (It just diverges faster), so 10 diverges.

6, you can't know if it converges or not, since it's not in the radius of convergence, and isn't bigger than 7. So, with the data you have, it's not possible to determine if it converges.

Sorry for the late answer, was eating dinner. :)

Answer 12

Although, for what I said to be valid, you must know (Not just believe) it to be valid! Therefore, I urge you to read about series and convergence radii. ;D

Answer 13

Thank you sooooo much!

Answer 14

Happy you were able to get help @megannicole51

Answer 15

thanks:)