Question

Determine whether the sequence converges or diverges. If it converges, find the limit. (If the sequence diverges, enter DIVERGES.) [ egin{array}{r} a_{n}=frac{3 n !}{2^{n}} \ lim _{n ightarrow infty} a_{n}= end{array} ]

          Determine whether the sequence converges or diverges. If it converges, find the limit. (If the sequence diverges, enter DIVERGES.)
[
egin{array}{r}
a_{n}=frac{3 n !}{2^{n}} \
lim _{n 
ightarrow infty} a_{n}=
end{array}
]

$Determine whether the sequence converges or diverges. If it converges, find the limit. (If the sequence diverges, enter DIVERGES.) [ eginarrayr an=frac3 n !2^n lim n ightarrow infty an= endarray ]$

Added by Fhyyd F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hoan Nguyen

05/03/2023

Step 1

The ratio test states that if the limit of the ratio of consecutive terms is less than 1, then the series converges, and if it's greater than 1, it diverges. Let's find the limit of the ratio of consecutive terms: \[\lim_{n \rightarrow \infty} \frac{a_{n+1}}{a_n} Show more…

Show all steps