$解:∵f(n)+f(\frac{1}{n})=\frac{n^2}{1+n^2}=\dfrac {(\frac {1}{n})^2}{1+(\frac {1}{n})^2}=\frac{n^2}{1+n^2}+\frac{1}{1+n^2}=1,$
$∴原式=\frac{1}{2}+\left[f(2)+f(\frac{1}{2})\right]+\left[f(3)+f(\frac{1}{3})\right]+···+\left[f(n+1)+f(\frac{1}{n+1})\right]=\frac{1}{2}+1×n=\frac{1}{2}+n.$