Does this sequence converge?

batonkirby

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Feb 26, 2021
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Does a_n converge (The problem is attached as an image)??

I think I'm supposed to find the limit as n approaches infinity for a_n, but I'm not sure how to evaluate that limit.

Could someone help me out?
 

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e^n = e*e*e*e...*e
(n+1)! = 2*3*4*5*....(n+1)

What trouble are you having finding this limit? After the 1st term in the fractions, the denominator is larger than the numerator which is always e.
 
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