Question

x  × (\(\dfrac{2}{4}\)+\(\dfrac{2}{12}\)+\(\dfrac{2}{24}\)+...+\(\dfrac{2}{180}\))=\(\dfrac{9}{10}\)

Answer 1

`x xx ( 2/4 + 2/12 + 2/24 +... + 2/180) = 9/10`

` x xx ( 1/2 + 1/6 + 1/12 + .... + 1/90) = 9/10`

\(x\times\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+....+\dfrac{1}{9.10}\right)=\dfrac{9}{10}\)

\(x\times\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+.....+\dfrac{1}{9}-\dfrac{1}{10}\right)=\dfrac{9}{10}\)

\(x\times\left(1-\dfrac{1}{10}\right)=\dfrac{9}{10}\)

\(x\times\dfrac{9}{10}=\dfrac{9}{10}\)

\(x=\dfrac{9}{10}:\dfrac{9}{10}=1\)

Vậy ` x = 1`

Answer 2

`x  × ( 2/4 + 2/12 + 2/24 +...+ 2/180 )=9/10`

`x  × ( 1/2+1/6+1/12+...+1/90 )=9/10`

`x xx ( 1/(1xx2)+1/(2xx3)+1/(3xx4)+...+1/(10xx9) )=9/10`

`x xx ( 1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10)=9/10`

`x xx(1-1/10)=9/10`

`x xx 9/10=9/10`

`x=9/10:9/10`

`x=1`