I. Multiple Choice
This section consists of 6 questions, each offering four options: (A), (B), (C), and (D). Only one of these options is correct. Please write the letter representing the correct answer in the parentheses after the question.
1. For each natural number $n$, the parabola $y=\left(n^{2}+n\right) x^{2}-(2 n+1) x+1$ intersects the $x$-axis at points $A_{n}, B_{n}$. Let $\left|A_{n} B_{n}\right|$ denote the distance between these two points. Then the value of $\left|A_{1} B_{1}\right|+\left|A_{2} B_{2}\right|+\cdots+\left|A_{1992} B_{1992}\right|$ is
(A) $\frac{1991}{1992}$
(B) $\frac{1992}{1993}$
(C) $\frac{1991}{1993}$
(D) $\frac{1993}{1992}$
(B)
I. Multiple Choice Question
1.【Analysis and Solution】 $\because y=(n x-1)[(n+1) x-1]$, when $y=0$, we get
$$
\begin{array}{l}
\quad x_{1}=\frac{1}{n}, x_{2}=\frac{1}{n+1} . \\
\therefore \quad\left|A_{n} B_{n}\right|=\frac{1}{n}-\frac{1}{n+1} . \\
\quad \text { Therefore, }\left|A_{1} B_{1}\right|+\left|A_{2} B_{2}\right|+\cdots+\left|A_{1992} B_{1992}\right| \\
\quad=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\cdots+\left(\frac{1}{1992}-\frac{1}{1993}\right) \\
\quad=1-\frac{1}{1993} \\
=\frac{1992}{1993} .
\end{array}
$$