Find the limit of the following sequence or determine that the sequence diverges. {tan an+8 9n -1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The limit of the sequence is (Type an exact answer.) OB. The sequence diverges.
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6.
![**Limit of a Sequence – Educational Exercise**
**Problem Statement:**
Find the limit of the following sequence or determine that the sequence diverges.
\[
\left\{
\tan^{-1} \left( \frac{9n}{9n + 8} \right)
\right\}
\]
**Instructions:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- ☐ **A.** The limit of the sequence is \[ \ \] .
(Type an exact answer.)
- ☐ **B.** The sequence diverges.
This problem requires you to determine the behavior of the sequence involving an inverse tangent function as the term index \( n \) approaches infinity. The sequence given is \(\left\{ \tan^{-1} \left( \frac{9n}{9n + 8} \right) \right\} \).
Use mathematical techniques such as limits, properties of inverse trigonometric functions, and asymptotic analysis to solve this problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ae82246-2ba7-4804-abb5-6328a4c1ee5a%2F1f018f7d-7543-48b4-85e8-144521c94755%2F25c7sjr.jpeg&w=3840&q=75)
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