MathDB

Parabola Problem

Source: 1992 National High School Mathematics League, Exam One, Problem 1

February 26, 2020

conicsparabola

Problem Statement

For any positive integer

n

A_n

and

B_n

are intersection of parabola

y=(n^2+n)x^2-(2n+1)x+1

and

x

-axis. Then, the value of

|A_1B_1|+|A_2B_2|+\cdots+|A_{1992}B_{1992}|

\text{(A)}\frac{1991}{1992}\qquad\text{(B)}\frac{1992}{1993}\qquad\text{(C)}\frac{1991}{1993}\qquad\text{(D)}\frac{1993}{1992}