Question

[Cỏ Bốn Lá]

Tính A = \(\frac{M}{N}\)biết 
M =\(\frac{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{99}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}}\)
N = \(N=\frac{92-\frac{1}{9}-\frac{2}{10}-\frac{3}{11}-...-\frac{90}{98}-\frac{91}{99}-\frac{92}{100}}{\frac{1}{45}+\frac{1}{50}+\frac{1}{55}+...+\frac{1}{495}+\frac{1}{500}}\)
 

Answer 1

[Nguyễn Thị Thùy Giang]

M=100

Xét tử N

92-(1/9)-(2/10)-(3/11)- ... -(90/98)-(91/99)-(92/100)

=(1+1+1+...+1)-(1/9)-(2/10)-(3/11)- ... -(90/98)-(91/99)-(92/100)

=1-(1/9)+1-(2/10)+1-(3/11)+......+1-(90/98)+1-(91/99)+1-(92/100)

=(8/9)+(8/10)+(8/11)+ ...+ (8/98)+(8/99)+(8/100)

=8.[(1/9)+(1/10)+(1/11)+...+(1/98)+(1/99)+(1/100)]

=40[(1/45)+(1/50)+(1/55)+...+(1/495)+(1/500)]

=>N=40

=>M/N=5/2