Power Series(Radius and interval of convergence)

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Homework Help Overview

The discussion revolves around determining the radius and interval of convergence for a power series, specifically focusing on the calculations involving the ratio test and the implications of the results.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the calculation of the radius of convergence using the ratio test, with some questioning the original poster's conclusion of R = 1/8. There are discussions about the limits involved in the ratio and the implications of having n! in the denominator.

Discussion Status

The conversation includes attempts to clarify the radius of convergence, with some participants suggesting that the original calculation may be incorrect. There is a recognition that the series converges for all x, but the terminology around infinity is discussed for clarity.

Contextual Notes

Participants are navigating the definitions and implications of convergence, particularly regarding the limits of the interval of convergence and the nature of infinity in this context.

naspek
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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..
please help me..
 

Attachments

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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?
 
Dick said:
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
 
naspek said:
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
 
naspek said:
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..
 
naspek said:
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?
 
  • #10
It converges for ALL x, that's what you mean, right? There's no such number as +infinity or -infinity. They are only limits you approach. You don't have to check them.
 
  • #11
alright! i understand now..
Thanks Dick =)
 

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