hjjklloppo

1/1.3 + 1/3.5 + 1/5.7 + ... +1/x.(x+2)

= 1/2.(1/1 - 1/3) + 1/2.(1/3 - 1/5) + 1/2.(1/5 - 1/7) + ... + 1/2.(1/x -1/x+2)

= 1/2.(1/1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/x - 1/x+2 )

= 1/2.(1/1 - 0 - 1/x+2 )

= 1/2 . ( 1/1 - 1/x+2 )

= 1/2 . ( x+2/x+2 - 1/x+2 )

= 1/2 . x+1/x+2

Mà 1/1.3 + 1/3.5 + 1/5.7 + ... +1/x.(x+2) = 5/11

=> 1/2 . x+1/x+2 = 5/11

=> x+1/x+2 = 5/11 : 1/2

=> x+1/x+2 = 10/11

=> x+1/x+2-1 = 10/11-1

=> x+1/x+1 = 10/10

=> x + 1 = 10

=> x = 10 - 1

=> x = 9

Vậy x = 9