Question

The nth term of a sequence is represented by 3n4−10/6n4+7 . What is the limit of the the nth term as n becomes increasingly large?

Answer 1

1/2

Explanation:

Given the limit of the function expressed as;

`\lim_(n \to \infty) (3n^4-10)/(6n^4+7) \\`

To take the limit, we nee to divide through by the highest power of n first

`\lim_(n \to \infty) (3n^4/n^4-10/n^2)/(6n^4/n^4+7/n^4)\\= \lim_(n \to \infty) (3-10/n^2)/(6+7/n^4)\\= (3-10/(\infty)^2)/(6+7/(\infty)^4)\\= (3-0)/(6-0)\\= (3)/(6)\\ = (1)/(2)\\`

Hence the limit of the the nth term as n becomes increasingly large is 1/2