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Tricky series radius of convergence question (analysis course)

  • Thread starter pcvt
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  • #1
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Homework Statement


Find the radius of convergence of sum from 1 to n of

1/(n^n) * x^(2^n)


Homework Equations





The Attempt at a Solution


Clearly ratio test isn't going to work straight away. I'm not sure how to deal with the 2^n exponent
 

Answers and Replies

  • #2
hunt_mat
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What about the nth root test?
 
  • #3
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From there I get down to finding for what values the limsup of 1/n x^(2^n/n) is less than one for

I believe its |x|<=1 but I'm not sure how to analytically prove this
 
  • #4
Dick
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From there I get down to finding for what values the limsup of 1/n x^(2^n/n) is less than one for

I believe its |x|<=1 but I'm not sure how to analytically prove this
I don't think |x|=1 works. But the case |x|<1 is easy. And |x|>1 is not much harder, you just want to show it diverges somehow. I'd say the easiest way is to combine l'Hopital or a ratio test with a comparison test. For example, can you show 2^n/n>n for large enough values of n?
 
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