Answer
Error: 4th line
Correct answer: $0$
Work Step by Step
The error is in the $4$th line: when evaluating limits towards infinity you must divide each term by the highest degree in the denominator:
$\displaystyle\lim_{n\to\infty} \frac{2n+2}{n^2}= \frac{\frac{2n}{n^2}+\frac{2}{n^2}}{\frac{n^2}{n^2}} =\displaystyle\lim_{n\to\infty} \frac{\frac{2}{n}+\frac{2}{n^2}}{1}=\frac{\displaystyle\lim_{n\to\infty}\frac{2}{n}+\displaystyle\lim_{n\to\infty}\frac{2}{n^2}}{1}=\frac{0+0}{1}=0$
