Consider the difference below for $m \geq 5$:
\[\sum_{n=1}^{m-1} \frac{1}{(1+n)^{2}}-\int_{x=1}^{m} \frac{1}{(1+x)^{2}} d x .\]
Which statement about the difference is $\text{TRUE}?$
- It is positive for infinitely many $m \geq 5$ and negative for infinitely many $m \geq 5$
- It is positive for all $m \geq 5,$ and is increasing as $m$ increases
- It is negative for finitely many $m \geq 5$ and is positive for infinitely many $m$
- It is positive for all $m \geq 5,$ and is decreasing as $m$ increases
- It is negative for all $m \geq 5$