Question

Cho A= 92 - 1/9 - 2/10 - 3/11 -....- 92/100 và B= 1/45 + 1/50 + 1/55 +.....+ 1/500.Tính A/B

Answer 1

\(A=92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}-...-\dfrac{92}{100}\)

\(=\left(1-\dfrac{1}{9}\right)+\left(1-\dfrac{2}{10}\right)+\left(1-\dfrac{3}{11}\right)+...+\left(1-\dfrac{92}{100}\right)\)

\(=\dfrac{8}{9}+\dfrac{8}{10}+...+\dfrac{8}{100}\)

\(=8\left(\dfrac{1}{9}+\dfrac{1}{10}+...+\dfrac{1}{100}\right)\)

\(B=\dfrac{1}{45}+\dfrac{1}{50}+...+\dfrac{1}{500}=\dfrac{1}{5}\left(\dfrac{1}{9}+\dfrac{1}{10}+...+\dfrac{1}{100}\right)\)

\(\dfrac{A}{B}=\dfrac{8\left(\dfrac{1}{9}+\dfrac{1}{10}+...+\dfrac{1}{100}\right)}{\dfrac{1}{5}\left(\dfrac{1}{9}+\dfrac{1}{10}+...+\dfrac{1}{100}\right)}\)

\(=8:\dfrac{1}{5}=40\)