Đáp án:
Giải thích các bước giải:
a) `(1-1/4).(1-1/9).(1-1/16)...(1-1/100)`
`=3/4*8/9*15/16*...*99/100`
`=(3.8.15...99)/(4.9.16...100)`
`=(1.3.2.4.3.5...9.11)/(2.2.3.3.4.4...10.10)`
`=((1.2.3...9).(3.4.5...11))/((2.3.4...10).(2.3.4...10))`
`=(1.11)/10.2`
`=11/20`
b) $\dfrac{\dfrac23+\dfrac2{15}+\dfrac2{21}}{\dfrac34+\dfrac3{20}+\dfrac3{28}}\\=\dfrac{\dfrac{8}{12}+\dfrac{8}{60}+\dfrac{8}{84}}{\dfrac{9}{12}+\dfrac{9}{60}+\dfrac{9}{84}}\\=\dfrac{8.\left(\dfrac{1}{12}+\dfrac{1}{60}+\dfrac{1}{84}\right)}{9.\left(\dfrac{1}{12}+\dfrac{1}{60}+\dfrac{1}{84}\right)}\\=\dfrac{8}{9}$
