Tinh nhanh 1 1 1 1 ____+_____+_______........______ 1*2 2*3 3*4 9*10
2 câu trả lời
`1/(1.2) + 1/(2.3) + 1/(3.4) + .... + 1/(9.10)`
`= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/9 - 1/10`
`= 1 - ( 1/2 - 1/2 ) - ( 1/3 - 1/3 ) - ..... - ( 1/9 - 1/9 ) - 1/10`
`= 1 - 0 - 0 - ........ - 0 - 1/10`
`= 1 - 1/10`
`= 9/10`
$\dfrac{1}{1×2}$ `+` $\dfrac{1}{2×3}$ `+` $\dfrac{1}{3×4}$ `+ ...... +` $\dfrac{1}{9×10}$
`=` $\dfrac{1}{1}$ `-` $\dfrac{1}{2}$ `+` $\dfrac{1}{2}$ `-` $\dfrac{1}{3}$ `+` $\dfrac{1}{3}$ `-` $\dfrac{1}{4}$ `+ ... +` $\dfrac{1}{9}$ `-` $\dfrac{1}{10}$
`=` $\dfrac{1}{1}$ `-` $\dfrac{1}{10}$
`=` $\dfrac{9}{10}$
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