Thursday, 21 May 2015

calculus - How can I calculate the limit of exponential divided by factorial?




I suspect this limit is 0, but how can I prove it?



limn+2nn!


Answer




The easiest way to do this is to do the following: Assume n4. Then 02nn!=ni=12i=222123ni=42i86ni=124=862n3.

Applying the squeeze theorem gives the result.


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