+5 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.
+118608 2n^4−15/6n^4+17
\(\displaystyle \lim_{n\rightarrow \infty}\;\;\frac{2n^4−15}{6n^4+17}\\ \qquad \text{At an educated guess I would say 2/6 = 1/3}\\ \qquad \text{But I should be more mathematical about it}\\~\\ \text{divide through by n^4 top and bottom}\\~\\ \displaystyle \lim_{n\rightarrow \infty}\;\;\frac{2−\frac{15}{n^4}}{6+\frac{17}{n^4}}\\~\\ =\frac{2}{6}\\ =\frac{1}{3} \)
