(1/2 + 1/6 +1/12 +.....+1/90):x = 9/20 help meeeeeeeeeeeeeeeeeeeeee

Ta có :

 $\text{$\dfrac{1}{2}$ + $\dfrac{1}{6}$ + $\dfrac{1}{12}$ +...+ $\dfrac{1}{90}$}$

$\text{= $\dfrac{1}{1 \times 2}$ + $\dfrac{1}{2 \times 3}$ + $\dfrac{1}{3 \times 4}$ +...+ $\dfrac{1}{9 \times 10}$}$

$\text{= 1 - $\dfrac{1}{2}$ + $\dfrac{1}{2}$ - $\dfrac{1}{3}$ + $\dfrac{1}{3}$ - $\dfrac{1}{4}$ +...+ $\dfrac{1}{9}$ - $\dfrac{1}{10}$}$

$\text{= 1 - $\dfrac{1}{10}$}$

$\text{= $\dfrac{9}{10}$}$

$\Rightarrow$ $\text{$\dfrac{9}{10}$ : x = $\dfrac{9}{20}$}$

$\Rightarrow$ $\text{x = $\dfrac{9}{10}$ : $\dfrac{9}{20}$}$

$\Rightarrow$ $\text{x = 2}$

Vậy $\text{x = 2}$

Đáp án:

Đặt `A=(1/2 +1/6 +1/12+......+1/90) : x =9/20`

       `A=(1/(1xx2) + 1/(2xx3) +.........+ 1/(9xx10)) : x =9/20`

       `A=(1 - 1/2 + 1/2 - 1/3 +1/3 - 1/4 +........+1/9 - 1/10) : x =9/20`

       `A=(1 - 1/10) : x =9/20`

       `A=9/10 : x = 9/20`

       `⇒x= 9/10 : 9/20`

       `⇒x=2`