Đáp án + Giải thích các bước giải:
Bài `1` :
`a)\frac{3}{5}x-\frac{1}{2}=\frac{-7}{10}`
`→\frac{3}{5}x=\frac{-7}{10}+\frac{1}{2}`
`→\frac{3}{5}x=\frac{-1}{5}`
`→3x=-1`
`→x=-\frac{1}{3}`
`--------------`
`b)\frac{2}{3}+\frac{3}{4}.\frac{1}{x}=\frac{-1}{6}`
`→\frac{3}{4x}=-\frac{2}{3}+(\frac{-1}{6})`
`→\frac{3}{4x}=-\frac{5}{6}`
`→3(-6)=5.4x`
`→-18=20x`
`→x=-\frac{9}{10}`
Bài `2` :
Ta có :
`(\frac{1}{10}-1)(\frac{1}{11}-1)(\frac{1}{12}-1)....(\frac{1}{2012}-1)`
`=(-\frac{9}{10})(-\frac{10}{11})(-\frac{11}{12})....(-\frac{2011}{2012})`
`=-\frac{9.10.11....2011}{10.11.12....2012}`
`=-\frac{9}{2012}`
Bài `3` :
Ta có :
`\frac{1}{501}<\frac{1}{500}`
`\frac{1}{502}<\frac{1}{500}`
`\frac{1}{503}<\frac{1}{500}`
`..................`
`\frac{1}{1000}<\frac{1}{500}`
`→\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+....+\frac{1}{1000}<\frac{1}{500}+\frac{1}{500}+\frac{1}{500}+....+\frac{1}{500}`
`→\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+....+\frac{1}{1000}<\frac{500}{500}`
`→\frac{1}{501}+\frac{1}{502}+\frac{1}{503}+....+\frac{1}{1000}<1` ( Điều Phải Chứng Minh )
