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 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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