Question

Answer 1

1: Gọi các phân số cần tìm có dạng là x/12

Theo đề, ta có: \(\dfrac{-1}{2}< \dfrac{x}{12}< \dfrac{-1}{12}\)

=>-6<x<-1

hay \(x\in\left\{-5;-4;-3;-2\right\}\)

Tổng là -14/12=-7/6

2: \(A=1+\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+\dfrac{1}{8\cdot10}+\dfrac{1}{10\cdot12}\)

\(=1+\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{12}\right)\)

\(=1+\dfrac{1}{2}\cdot\dfrac{5}{12}=1+\dfrac{5}{24}=\dfrac{29}{24}\)