# Power Series(Radius and interval of convergence)

hey there..
i've try this question(attachment) already...
i got radius of convergence, R = 1/8

at x = 1/8,
converges...

at x = -1/8
i don't how to do this one..

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## Answers and Replies

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Dick
Homework Helper
How did you conclude that has radius of convergence 1/8?? Your bmp has an n! in the denominator. What does the ratio test tell you?

How did you conclude that has radius of convergence 1/8?? Your bmp has an n! in the denominator. What does the ratio test tell you?
to find the radius, r..
i use an / an+1

Dick
Homework Helper
to find the radius, r..
i use an / an+1
Go ahead. Use it. What the limit of the ratio?

then.. i got radius = 1/8

Dick
Homework Helper
then.. i got radius = 1/8
What's the ratio an/an+1? I don't think you are getting that limit right.

i've revised back my calculation..
should i get infinity for my radius..

Dick
Homework Helper
i've revised back my calculation..
should i get infinity for my radius..
Yes.

ok.. so.. i need to check the interval of convergence..

when x = infinity,
the series will converges..

when c = -infinity,
the series will converges too..

hence, my interval of convergence is (-infinity,infinity)

am i right?

Dick