
#1
May2704, 07:53 AM

P: 199

[tex]
\sum_{k=1}^\infty (\sqrt{k+1}  \sqrt{k})(\ln{k+1}\ln{k}) [/tex] How do I go about finding out if it's convergent or divergent ? 



#2
May2704, 08:14 AM

Sci Advisor
HW Helper
PF Gold
P: 12,016

[tex] \sum_{k=1}^\infty (\sqrt{k+1}  \sqrt{k})(\ln{(k+1)}\ln{k}) [/tex]? 



#4
May2704, 08:53 AM

Sci Advisor
HW Helper
P: 9,398

investigate sum
Hint: sqrt(k+1)sqrt(k) = {sqrt(k)+sqrt(k+1)}^{1}
and you can put the logs together. 



#6
May2704, 09:46 AM

P: 2

after combining the logs, try to prove that
[tex]\frac{1}{x} \geq \ln (1 + \frac{1}{x})[/tex] for all positive x edit: oops i missed the last reply while typing mine sorry 


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