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srl17

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## Homework Statement

Prove that [itex] \sum\limits_{n = 0}^\infty {\frac{{\left( { \sqrt{n+1} \right) - \sqrt{n} }}{{\left( {\sqrt{n}} \right)!}}}[/itex]

is divergent

## Homework Equations

## The Attempt at a Solution

This is an intro to analysis course. We haven't gone over the integral test which would be wonderful here. I have tried the limit comparison w/ 1/n^1/2, ratio and root test which were all inconclusive. I thought of using the comparison test but 1/n^(1/2) is bigger.

I am thinking of using Cauchy Criterion for Series and proving that the partial sums are monotone increasing and unbounded, but how would I prove it is unbounded?

Or If anyone sees a simpler way than Cauchy I am all eyes.

And this is my first attempt at using latex so I hope the equation turns out right, if not sorry and reference the subject title. Thank you!

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