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**1. The problem statement, all variables and given/known data**

[tex]\sum(\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2})}

^{k}[/tex]

as k [tex]\rightarrow[/tex][tex]\infty[/tex]

**2. Relevant equations**

Root test: (a

_{k})

^{1/k}

**3. The attempt at a solution**

(a

_{k})

^{1/k}= (\frac{1}{\sqrt{ln k +2}-\sqrt{ln k -2})

does it equal 0? since 1/[tex]\infty[/tex] = 0

but its [tex]\infty[/tex] - [tex]\infty[/tex] i would have to use l'Hôpital's rule right?