is this correct ### Understanding Limits in Sequences**Problem Statement:**The \(n\)th term of a sequence is represented by the fraction:\[ \frac{2n^4 + 25n^2 + 32n - 15}{6n^4 + 2n^3 - 11n^2 - 2n + 17} \]**Question:**What is the limit of the \(n\)th term as \(n\) becomes increasingly large?### Options:- \( \circ \) 0- \( \circ \) \(\frac{1}{3}\)- \( \circ \) 3 - \( \circ \) The limit does not exist.### Solution:To find the limit of the given sequence as \( n \) approaches infinity, observe the highest power of \( n \) in both the numerator and the denominator. The highest power in the numerator is \( n^4 \) (with a coefficient of 2), and in the denominator, it is also \( n^4 \) (with a coefficient of 6). When considering the limit, the terms with the highest power dominate the behavior of the function. Therefore, we can approximate the fraction for large \( n \) as:\[ \frac{2n^4}{6n^4} = \frac{2}{6} = \frac{1}{3} \]So, as \( n \) becomes increasingly large, the \( n \)th term of the sequence approaches \( \frac{1}{3} \).### Answer:\( \boxed{\frac{1}{3}} \)

Name: is this correct ### Understanding Limits in Sequences**Problem Stateme
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: is this correct ### Understanding Limits in Sequences**Problem Statement:**The \(n\)th term of a sequence is represented by the fraction:\[ \frac{2n^4 + 25n^2 + 32n - 15}{6n^4 + 2n^3 - 11n^2 - 2n + 17} \]**Question:**What is the limit of the \(n\)th