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2024
2612
a,
( 1 - $\dfrac{1}{2}$ ) . ( 1 - $\dfrac{1}{3}$ ) . ( 1 - $\dfrac{1}{4}$ ) . ... . ( 1 - $\dfrac{1}{100}$
= $\dfrac{1}{2}$ . $\dfrac{2}{3}$ . $\dfrac{3}{4}$ . ... . $\dfrac{99}{100}$
= $\dfrac{1 \times 2 \times 3 \times ... \times 99}{2 \times 3 \times 4 \times ... \times 100}$
=$\dfrac{1}{100}$
b,
$\dfrac{10}{56}$ + $\dfrac{10}{140}$ + $\dfrac{10}{260}$ + ... + $\dfrac{10}{1400}$
= $\dfrac{5}{28}$ + $\dfrac{5}{70}$ + $\dfrac{5}{130}$ + ... + $\dfrac{5}{700}$
= 5 . ( $\dfrac{1}{28}$ + $\dfrac{1}{70}$ + $\dfrac{1}{130}$ + ... + $\dfrac{1}{700}$ )
= 5 . ( $\dfrac{1}{4.7}$ + $\dfrac{1}{7.10}$ + $\dfrac{1}{10.13}$ + ... + $\dfrac{1}{25.28}$ )
= 5 . $\dfrac{1}{3}$ . ( $\dfrac{1}{4.7}$ + $\dfrac{1}{7.10}$ + $\dfrac{1}{10.13}$ + ... + $\dfrac{1}{25.28}$ )
= $\dfrac{5}{3}$ . ( $\dfrac{3}{4.7}$ + $\dfrac{3}{7.10}$ + $\dfrac{3}{10.13}$ + ... + $\dfrac{3}{25.28}$ )
= $\dfrac{5}{3}$ . ( $\dfrac{1}{4}$ - $\dfrac{1}{28}$ )
= $\dfrac{5}{3}$ . $\dfrac{3}{14}$
= $\dfrac{5}{14}$
Hãy giúp mọi người biết câu trả lời này thế nào?
Đáp án:
Giải thích các bước giải:
`a) (1-1/2).(1-1/3).(1-1/4). ... .(1-1/100)`
`=(2/2-1/2).(3/3-1/3). ... .(100/100-1/100)`
`=1/2 . 2/3. ... .99/100`
`=1/100`
`b) 10/56+10/140+10/260+.....+10/1400`
`= 5/28+ 5/70+5/130+..+ 5/700`
`= 5/4.7+ 5/7.10+5/10.13+...+ 5/25.28`
`= 5.( 1/4.7+ 1/7.10+ 1/10.13+...+ 1/25.28)`
`= 5/3 .( 3/4.7+ 3/7.10+ 3/10.13+...+ 3/25.28)`
`= 5/3.( 1/4- 1/7+ 1/7- 1/10+...+ 1/25- 1/28)`
`= 5/3.( 1/4- 1/28)`
`=5/3 . 3/14`
`=5/14`
Hãy giúp mọi người biết câu trả lời này thế nào?
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