Question

若点P(a,2)与点Q(-3,b)关于x轴对称,求代数式1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+......1/(a-10)(b-10)的值

速度速度

Answer 1

因为点P(a,2)与点Q(-3,b)关于x轴对称
所以a=-3，b=-2
所以1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+......+1/(a-10)(b-10)
　　=1/[(-3)×(-2)]+1/[(-4)×(-3)]+1/[(-5)×(-4)]+……+1/[(-13)×(-12)]
　　=1/(3×2)+1/(4×3)+1/(5×4)+……+1/(13×12)
　　=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/12-1/13)
　　=1/2-1/13
　　=11/26