Test for conver

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: (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/[tex]\infty[/tex] = 0
but its [tex]\infty[/tex] - [tex]\infty[/tex] i would have to use l'Hôpital's rule right?
 

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
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No, I would rationalize the denominator. L'Hopital won't be necessary.
 
Then i would get

[tex]\frac{\sqrt{ln k + 2} + \sqrt{ln k - 2}}{4}[/tex]

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

Tom Mattson

Staff Emeritus
Science Advisor
Gold Member
5,453
21
That's what I got.
 
thanks
 

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