Determine whether the nonincreasing sequence converges or diverges.
-$$a _ { n } = \frac { 1 + \sqrt { 3 n } } { n }$$
A) Converges
B) Diverges

Question

Quizplus · Accepted Answer

We can use the limit comparison test with the sequence $\frac{1}{n}$ which is a known divergent sequence. 
$$\lim_{n	o\infty}\frac{\frac{1+\sqrt{3n}}{n}}{\frac{1}{n}}=\lim_{n	o\infty}(1+\sqrt{3n})=\infty$$
Since the limit is greater than zero, and the sequence $\frac{1}{n}$ is known to diverge, we conclude that the sequence $a_n$ also diverges. Therefore, the answer is A.

Determine Whether the Nonincreasing Sequence Converges or Diverges an=1+3nna _ { n } = \frac { 1 + \sqrt { 3 n } } { n }an​=n1+3n​​

Determine Whether the Nonincreasing Sequence Converges or Diverges $a _ { n } = \frac { 1 + \sqrt { 3 n } } { n }$