Calculate the limit of the sequence
lim
knowing that
\ a_n = \frac{3^n}{n!},n\geqslant1
Choose the right answer:
a) 1
b) 0
c) 3
d) \frac{1}{3}
e) 2
f) \frac{1}{2}
Answer
Using D'Alambert's criterion, we can see that
\lim_{n \to \infty}\frac{a_{n+1}}{a_n}=\lim_{n \to \infty} \frac{3^{n+1}n!}{3^{n}(n+1)!}= \lim_{n \to \infty} \frac{3}{n+1}=0
Thus, \lim\limits_{n \to \infty} a_n =0.
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