Calculate the limit of the sequence
limn→∞ an,n⩾1
knowing that
an=3nn!,n⩾1
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
limn→∞an+1an=limn→∞3n+1n!3n(n+1)!=limn→∞3n+1=0
Thus, limn→∞an=0.
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