Science:Math Exam Resources/Courses/MATH105/April 2014/Question 06 (b)/Hint 2

By the Divergence Test, we must have that the terms of $\frac{n{a}_n-2n+1}{n+1}$ approach zero as $n\to \mathrm{\infty }$. Thus, $\underset{n\to \mathrm{\infty }}{\lim }\frac{n{a}_n-2n+1}{n+1}=0$. Can you use this to obtain more information about the terms of $a_n$?