Question

[Lý Minh Ngọc]

a) Cho A=(1/2-1)(1/3-1).....(1/200-1). hãy so sánh A với -1/199

b) Tính B=1+1/2(1+2)+1/3(1+2+3)...+1/500(1+2+3+...+500)

Answer 1

[Nguyễn Phương Uyên]

a, \(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{200}-1\right)\)

\(-A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{200}\right)\)

\(-A=\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{199}{200}\)

\(-A=\frac{1}{200}\)

\(A=\frac{-1}{200}>\frac{-1}{199}\)