Limit of (n)^(.5)/ln n to Finding the Limit of a Sequence

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Homework Statement


How to find the limit of :
(n) ^(.5) / ln n


Homework Equations





The Attempt at a Solution



I tied doing it, I got inifity, is that right ?
 
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Yes. L'Hopital.
 
Uha, and what if I want determine the Convergence or Divergece of it ?

What test to use?

I think, that we should " limit of comparision test"
 
The limit comparison test is for series, not sequences.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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