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

a-the sequence diverges

Explanation:

edg 2023

Answer 2

Option (1)

Explanation:

Sequence has been given as,

`a_n=(n^3+3n)/(n^2-6n)`

`\lim_(n \to \infty)(n^3+3n)/(n^2-6n)`

`=\lim_(n \to \infty)((n^3+3n)/(n^3) )/((n^2-6n)/(n^3) )`

`=\lim_(n \to \infty)(1+(3)/(n^2))/((1)/(n)-(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.