Example 8. When $\mathrm{n}=1,2,3, \cdots, 1988$, find the sum $\mathrm{s}$ of the lengths of the segments cut off by the x-axis for all functions
$$
y=n(n+1) x^{2}-(2 n+1) x+1
$$
The function $y=n(n+1) x^{2}-(2 n+1) x+1$ intersects the axis at two points, the abscissas of which are the roots of the equation
$$
n(n-1) x^{2}-(2 n+1) x+1=0 \text { . }
$$

Transforming the above equation into
$$
(n x-1)[(n+1) x-1]=0,
$$

we solve to get $x_{1}=\frac{1}{n+1}, x_{2}=\frac{1}{n}$.
Thus, $\mathrm{d}=\left|\mathrm{x}_{2}-x_{1}\right|=\frac{1}{n}-\frac{1}{n+1}$.
Then the sum
$$
\begin{array}{l} 
s=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right) \\
+\cdots+\left(\frac{1}{1988}-\frac{1}{1989}\right) \\
= 1-\frac{1}{1989} \\
= \frac{1988}{1989} \\
\end{array}
$$