**Problem Statement:**Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)\[ a_n = \frac{n^2}{\sqrt{n^3 + 2n}} \]\[ \lim_{{n \to \infty}} a_n = \]**Instructions:**You are given a sequence defined by the formula \( a_n = \frac{n^2}{\sqrt{n^3 + 2n}} \). Your task is to evaluate the limit of the sequence as \( n \) approaches infinity. Determine if the sequence converges to a specific value or if it diverges. If it converges, provide the limiting value. If the limit does not exist, indicate this by entering "DNE" (Does Not Exist). **Note:**This problem requires understanding the behavior of sequences and limits as they approach infinity, often involving techniques like simplifying the expression or using L'Hopital's Rule if applicable.

Name: **Problem Statement:**Determine whether the sequence converges or div
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: **Problem Statement:**Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)\[ a_n = \frac{n^2}{\sqrt{n^3 + 2n}} \]\[ \lim_{{n \to \infty}} a_n = \]**Instructions:**You are gi