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The nth term of a sequence is represented by 2n^4−15/6n^4+17 .

What is the limit of the the nth term as n becomes increasingly large?

 

Options :

 

−13/23

 

1/3

 

3

 

The limit of the nth term does not exist.

 Feb 6, 2023
edited by Guest  Feb 6, 2023
edited by Guest  Feb 6, 2023
edited by Guest  Feb 6, 2023
 #1
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2n^4−15/6n^4+17

 

\(\displaystyle \lim_{n\rightarrow \infty}\;\;\frac{2n^4−15}{6n^4+17}\\ \qquad \text{At an educated guess I would say 2/6 = 1/3}\\ \qquad \text{But I should be more mathematical about it}\\~\\ \text{divide through by n^4 top and bottom}\\~\\ \displaystyle \lim_{n\rightarrow \infty}\;\;\frac{2−\frac{15}{n^4}}{6+\frac{17}{n^4}}\\~\\ =\frac{2}{6}\\ =\frac{1}{3} \)

 Feb 7, 2023

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