Đáp án:
`A=1/7`
`B=100/198`
`C=13/25`
Giải thích các bước giải:
`A=1^2/(1.2) . 2^2/(2.3) . 3^2/(3.4) . 4^2/(4.5) . 5^2/(5.6) . 6^2/(6.7)`
`=(1^2 . 2^2 . 3^2 . 4^2 . 5^2 . 6^2)/(1.2.2.3.3.4.4.5.5.6.6.7)`
`=(1.1.2.2.3.3.4.4.5.5.6.6)/(1.2.2.3.3.4.4.5.5.6.6.7)=1/7`
$\\$
`B=(1.3)/2^2 . (2.4)/3^2 ... (98.100)/99^2`
`=(1.3.2.4....98.100)/(2^2 . 3^2 ... 99^2)=(1.3.2.4....98.100)/(2.2.3.3...99)`
`=(1.2...98)/(2.3...99) . (3.4...100)/(2.3...99) = 1/99 . 100/2 = 100/198`
$\\$
`C=(1-1/4) . (1-1/9) ... (1-1/625)`
`=3/4 . 8/9 ... 624/625` ( có `24` số hạng )
`=(3.8...624)/(4.9...625)=(1.3.2.4...24.26)/(2.2.3.3...25.25)`
`=(1.2....24)/(2.3...25) . (3.4...26)/(2.3...25) = 1/25 . 26/2 = 13/25`
