Đáp án:
`a, x=28`
`b,x=1`
`c, x=17`
Giải thích các bước giải:
`a,`
`1/(1.4) + 1/(4.7) + ... + 1/(x (x+3) ) =10/31` (Điều kiện : `x\ne 0, x\ne -3`)
`-> 1/3 (1 - 1/4 + 1/4 - 1/7 + ... + 1/x - 1/(x+3) )=10/31`
`-> 1/3 (1 - 1/(x+3) )=10/31`
`-> 1 - 1/(x+3)=10/31 : 1/3`
`-> 1 - 1/(x+3)=10/31 . 3`
`-> 1 - 1/(x+3) = 30/31`
`->1/(x+3)=1-30/31`
`->1/(x+3)=31/31-30/31`
`->1/(x+3)=1/31`
`->x+3=31`
`->x=31-3`
`->x=28` (Thỏa mãn)
Vậy `x=28`
`b,`
`x-20/(11.13) - 20/(13.15) - ... - 20/(53.55)=3/11`
`-> x - (20/(11.13)+20/(13.15)+...+20/(53.55) )=3/11`
`-> x - 10(2/(11.13) + 2/(13.15) + ... + 2/(53.55) )=3/11`
`-> x-10 (1/11 - 1/13 + 1/13 - 1/15 + ... + 1/53 - 1/55)=3/11`
`->x-10 (1/11-1/55)=3/11`
`->x - 10 (5/55-1/55)=3/11`
`->x-10 . 4/55=3/11`
`->x-40/55=3/11`
`->x=3/11 + 40/55`
`->x=15/55 + 40/55`
`->x=1`
Vậy `x=1`
`c,`
`1/21 + 1/28 + ... + 2/(x (x+1) )=2/9` (Điều kiện : `x\ne 0, x\ne -1`)
`-> 2/42 + 2/56 + ... + 2/(x (x+1) )=2/9`
`-> 2 (1/42 + 1/56 + ... + 1/(x (x+1) ) )=2/9`
`-> 2 (1/(6.7) + 1/(7.8) + ... + 1/(x (x+1) ) ) = 2/9`
`-> 2 (1/6 - 1/7+ 1/7 - 1/8 + ... + 1/x - 1/(x+1) )=2/9`
`-> 2 (1/6 -1/(x+1)=2/9`
`-> 1/6 -1/(x+1)=2/9 : 2`
`->1/6 - 1/(x+1)=1/9`
`->1/(x+1)=1/6 -1/9`
`->1/(x+1) = 1/18`
`->x+1=18`
`->x=18-1`
`->x=17` (Thỏa mãn)
Vậy `x=17`
