\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+.....+\dfrac{1}{99.100}-x=-\dfrac{1}{100}\)
Xét : \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+......+\dfrac{1}{99.100}\)
`=1-1/2 + 1/2 - 1/3 + ..... + 1/90 - 1/100`
`=1 - 1/100`
`=100/100-1/100`
`=99/100`
Thay `99/100`
`=> 99/100 - x = -1/100`
`x=99/100 - (-1/100)`
`x= 99/100 + 1/100`
`x=(99+1)/100`
`x=100/100`
`x=1`
Vậy `x=1`
\(\rightarrow\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{99}-\dfrac{1}{100}\right)-x=-\dfrac{1}{100}\\ \rightarrow\left(1-\dfrac{1}{100}\right)-x=-\dfrac{1}{100}\\ \rightarrow\dfrac{99}{100}-x=-\dfrac{1}{100}\\ \rightarrow x=\dfrac{99}{100}-\left(-\dfrac{1}{100}\right)=\dfrac{99}{100}+\dfrac{1}{100}\\ \rightarrow x=\dfrac{100}{100}=1\)
