Đáp án:
250%
Giải thích các bước giải:
M = $\frac{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{99}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}$
M = $\frac{1+(\frac{1}{99}+1)+(\frac{2}{98}+1)+(\frac{3}{97}+1)+...+(\frac{98}{2}+1)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}$
M = $\frac{\frac{100}{100}+\frac{100}{99}+\frac{100}{98}+\frac{100}{97}+...+\frac{100}{2}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}$
M = $\frac{100.(\frac{1}{100}+\frac{1}{99}+\frac{1}{98}+...+\frac{1}{2})}{(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100})}$ = 100
N = $\frac{92-\frac{1}{9}-\frac{2}{10}-\frac{3}{11}-...-\frac{92}{100}}{\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{500}}$
N = $\frac{(1-\frac{1}{9})+(1-\frac{2}{10})+(1-\frac{3}{11})+...+(1-\frac{92}{100})}{\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{500}}$
N = $\frac{\frac{8}{9}+\frac{8}{10}+\frac{8}{11}+...+\frac{8}{100}}{\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{500}}$
N = $\frac{8(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100})}{\frac{1}{5}(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...+\frac{1}{100})}$ = $\frac{8}{\frac{1}{5}}$ =40
M : N = $\frac{100}{40}$ = 250%
