# Test for conver

#### magma_saber

1. The problem statement, all variables and given/known data
$$\sum(\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2})}k$$
as k $$\rightarrow$$$$\infty$$

2. Relevant equations
Root test: (ak)1/k

3. The attempt at a solution
(ak)1/k = (\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2})
does it equal 0? since 1/$$\infty$$ = 0
but its $$\infty$$ - $$\infty$$ i would have to use l'Hôpital's rule right?

#### Tom Mattson

Staff Emeritus
Gold Member
No, I would rationalize the denominator. L'Hopital won't be necessary.

#### magma_saber

Then i would get

$$\frac{\sqrt{ln k + 2} + \sqrt{ln k - 2}}{4}$$

as k approaches infinity, the function would also approach infinity so it diverges?

#### Tom Mattson

Staff Emeritus
Gold Member
That's what I got.

thanks

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