Question

Tìm thương A:B bt
A= 9/1+8/2+7/3+...+1/9

B=1/2+1/3+1/4+...+1/10

Answer 1

\(A=\)\(\frac{9}{1}+\frac{8}{2}+\frac{7}{3}+...+\frac{1}{9}\)

\(A=\left(\frac{9}{1}-8\right)+\left(\frac{8}{2}+1\right)+\left(\frac{7}{3}+1\right)+...+\left(\frac{1}{9}+1\right)\)

\(A=1+\frac{10}{2}+\frac{10}{3}+...+\frac{10}{9}\)

\(A=\frac{10}{10}+\frac{10}{2}+\frac{10}{3}+...+\frac{10}{9}\)

\(A=10\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}\right)>\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}=B\)

\(\Rightarrow A:B=\frac{10\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}}\)\(=10\)

Vậy \(A:B=10\)