find the limit of the following sequence or determine that the sequence diverges.\n{((2n + 1)!)/((2n)…
find the limit of the following sequence or determine that the sequence diverges.\n{((2n + 1)!)/((2n)! )}\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the limit of the sequence is \n(type an exact answer.)\nb. the sequence diverges.
Answer
Explanation:
Step1: Simplify the sequence term
Recall that $(m + 1)!=(m+1)\times m!$. So, $\frac{(2n + 1)!}{(2n)!}=\frac{(2n+1)\times(2n)!}{(2n)!}=2n + 1$.
Step2: Find the limit as n approaches infinity
We need to find $\lim_{n\rightarrow\infty}(2n + 1)$. As $n\rightarrow\infty$, the value of $2n+1$ also approaches infinity. That is, $\lim_{n\rightarrow\infty}(2n + 1)=\infty$.
Answer:
B. The sequence diverges.