- #1

Piamedes

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## Homework Statement

Test for convergence the series:

[tex] a_[n] = \frac{1}{n*n^{\frac{1}{n}}} [/tex]

## Homework Equations

Various Sequence Convergence Tests

## The Attempt at a Solution

So far I've tried both a normal comparison and limit comparison test with n^2. The normal one seemed fine until the end. Here was my logic:

For n greater than 1 (its just less than, not equal)

[tex] n^{\frac{1}{n}} \le n [/tex]

[tex] \frac{1}{n^{\frac{1}{n}}} \ge \frac{1}{n} [/tex]

[tex] \frac{1}{n*n^{\frac{1}{n}}} \ge \frac{1}{n^2}} [/tex]

But that doesn't work because it just proves that for every term, this sequence is greater than the p-series for n^2.

For the limit comparison test I don't get an actual limit, so I can't use it.

If anyone has any suggestions for which test to use, or what series to compare it to, I would be most grateful.