Question

Which statement describes the sequence defined by a Subscript n Baseline = StartFraction n cubed + 3 n Over n squared minus 6 n EndFraction?

Answer 1

Answer:

Option (1)

Step-by-step explanation:

Sequence has been given as,

$a_n=\frac{n^3+3n}{n^2-6n}$

$\lim_{n \to \infty}\frac{n^3+3n}{n^2-6n}$

$=\lim_{n \to \infty}\frac{\frac{n^3+3n}{n^3} }{\frac{n^2-6n}{n^3} }$

$=\lim_{n \to \infty}\frac{1+\frac{3}{n^2}}{\frac{1}{n}-\frac{6}{n^2} }$

= ∞

That means with the increase in the value of 'n' sequence gets larger and larger.

Therefore, sequence will diverge.

Option 1 will be the correct option.