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Power Series(Radius and interval of convergence)

  • Thread starter naspek
  • Start date
  • #1
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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

Answers and Replies

  • #2
Dick
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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?
 
  • #3
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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?
to find the radius, r..
i use an / an+1
 
  • #4
Dick
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to find the radius, r..
i use an / an+1
Go ahead. Use it. What the limit of the ratio?
 
  • #5
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then.. i got radius = 1/8
 
  • #6
Dick
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then.. i got radius = 1/8
What's the ratio an/an+1? I don't think you are getting that limit right.
 
  • #7
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i've revised back my calculation..
should i get infinity for my radius..
 
  • #8
Dick
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i've revised back my calculation..
should i get infinity for my radius..
Yes.
 
  • #9
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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
Dick
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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
181
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alright! i understand now..
Thanks Dick =)
 

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