- #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

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- Thread starter pcvt
- Start date

- #1

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

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

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

- #2

hunt_mat

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What about the nth root test?

- #3

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I believe its |x|<=1 but I'm not sure how to analytically prove this

- #4

Dick

Science Advisor

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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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