Câu hỏi của Nguyen Lan

Question

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

Chứng minh rằng M < 1/2

Dương Minh Uy · Accepted Answer

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

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

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

$M< \dfrac{1}{2}$Câu trả lời: $M=\dfrac{1}{1000}+\dfrac{1}{1002}+\dfrac{1}{1004}+...+\dfrac{1}{2000}$

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

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

$M< \dfrac{1}{2}$