Solve Please

lim(n->INF)

  n^2+1
----------
(n+1)^2+1

The mark scheme says it equals 1. But I also get a remainder of -2n-1.

What am I doing wrong?

this thread needs some tex

\lim_{n\to \infty}\frac{n^2+1}{(n+1)^2+1} = \lim_{n\to \infty}\frac{n^2+1}{n^2+2n+2}
=\lim_{n\to \infty}1 -\frac{2n+1}{n^2+2n+2} = \lim_{n\to \infty}1 -\frac{2+1/n}{n+2+2/n} = 1 + 0

or

\lim_{n\to \infty}\frac{n^2+1}{(n+1)^2+1} = \lim_{n\to \infty}\frac{n^2+1}{n^2+2n+2}
=\lim_{n\to \infty}\frac{1+1/n^2}{1+2/n+2/n^2} = \frac{1+0}{1+0+0}