Question

Determine whether the sequence converges or diverges. If it converges, find the limit. (if an answer does not exist, enter dne. ) an = n 6 sin(6/n).

Answer 1

Answer:

The sequence converges to 1

Step-by-step explanation:

Find the limit of the sequence as n approaches infinity

$\lim_{n \to \infty} \frac{n}{6}sin(\frac{6}{n})$

$\lim_{n \to \infty}\frac{sin(\frac{6}{n})}{\frac{6}{n}}$

$\lim_{n \to \infty}\frac{cos(\frac{6}{n})*-\frac{6}{n^2} }{-\frac{6}{n^2}}$

$\lim_{n \to \infty} cos(\frac{6}{n})$

$cos(0)$

$1$

Therefore, since the sequence approaches a limit of 1, then it converges.