Determine whether the following sequence is increasing or decreasing:
$$\frac{(n-8)^2}{(1-n)^2}, n\geq 2$$
So the first few terms are: $36,\frac{25}{4},\frac{16}{9},...$ so let's assume the sequence is decreasing.
$a_n\geq a_{n+1} \Leftrightarrow \frac{(n-8)^2}{(1-n)^2} \geq \frac{(n-7)^2}{n^2} \Leftrightarrow \frac{(n-8)^2n^2-(n-7)^2(1-n)^2}{(1-n)^2n^2}\geq 0$
The denominator is positive $\forall n\in\Bbb N$ so now I only have to prove that the numerator is non-negative. In other words, I have to prove that $(n-8)^2n^2\geq (n-7)^2(1-n)^2 $ What would be some smart move now to prove this?