Question

[Nguyen Lan]

Có: M = 1/1000 + 1/1002 + 1/1004 + ... + 1/1998 + 1/2000

Chứng minh rằng M < 1/2

Answer 1

[Dương Minh Uy]

\(M=\dfrac{1}{1000}+\dfrac{1}{1002}+\dfrac{1}{1004}+...+\dfrac{1}{2000}\)

\(2M=\dfrac{1}{500}+\dfrac{1}{501}+\dfrac{1}{502}+...+\dfrac{1}{1000}\)

\(2M< \dfrac{1}{500}+\dfrac{1}{500}+\dfrac{1}{500}+...+\dfrac{1}{500}=\dfrac{500}{500}=1\)

\(M< \dfrac{1}{2}\)