Thursday, 24 August 2017

Calculate the limit of the sequence limnrightarrowinftyan,ngeqslant1



Calculate the limit of the sequence




limn an,n1



knowing that



 an=3nn!,n1



Choose the right answer:



a) 1




b) 0



c) 3



d) 13



e) 2



f) 12


Answer




Using D'Alambert's criterion, we can see that



limnan+1an=limn3n+1n!3n(n+1)!=limn3n+1=0



Thus, limnan=0.


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