Question

[Khổng Thị Hải Yến]

Cho A=1/2+1/3+1/4+...+1/199+1/200

       B=1/199+2/198+3/197+...+198/2+199/1

Tính A : B

Answer 1

[Tran Le Khanh Linh]

\(B=\frac{1}{199}+\frac{2}{198}+\frac{3}{197}+....+\frac{198}{2}+\frac{199}{1}\)

\(=\left(\frac{1}{199}+1\right)+\left(\frac{2}{198}+1\right)+\left(\frac{3}{197}+1\right)+.....+\left(\frac{198}{2}+1\right)+\frac{200}{200}\)

\(=200\left(\frac{1}{100}+\frac{1}{199}+\frac{1}{198}+....+\frac{1}{2}\right)\)

= 200.A

=> A:B=\(\frac{1}{200}\)