Limit of 10^n/n as n-> infinity

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ayandas
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Hi,

Can anyone please suggest a solution to the problem:

lim 10n/(n!)
n->(infinite)
 
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When n is large, the numerator is much larger than the demoninator, so the limit is 0, surely?
 


Are you sure? When n is small, the numerator is larger, but when n gets large, the denominator is actually larger.

EDIT: Next time, put a question like this in the 'Homework Questions' section. That's where it should be, and you'll also probably get a response faster that way.
 


My bad, got the names the wrong way round ;)
 


No worries, just didn't want to confuse the OP!
 

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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