Bài 6.
a) `7/x + 4/5.9 + 4/9.13 + ... + 4/41.45 = 29/45`
`7/x + (1/5 - 1/9 + 1/9 - 1/13 + ... + 1/41 - 1/45) = 29/45`
`7/x + (1/5 - 1/45) = 29/45`
`7/x + 8/45 = 29/45`
`7/x = 29/45 - 8/45`
`7/x = 7/15`
`=> x = 15`
Vậy x = 15.
b) `x/2008 - 1/10 - 1/15 - 1/21 - ... - 1/120 = 5/8`
`x/2008 - (1/10 + 1/15 + 1/21 + ... + 1/120) = 5/8`
Đặt `A = 1/10 + 1/15 + 1/21 + ... + 1/120`
`=> 1/2A = 1/20 + 1/30 + 1/42 + ... + 1/240`
`= 1/4.5 + 1/5.6 + 1/6.7 + ... + 1/15.16`
`= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/15 - 1/16`
`= 1/4 - 1/16 = 3/16`
`=> A = 3/16 : 1/2 = 3/8`
`x/2008 - 3/8 = 5/8`
`x/2008 = 5/8 + 3/8`
`x/2008 = 1`
`=> x = 2008`
Vậy x = 2008.
c) 1/3.5 + 1/5.7 + 1/7.9 + ... + 1/(2x+1)(2x+3) = 15/93
=> 2/3.5 + 2/5.7 + 2/7.9 + ... + 2/(2x+1)(2x+3) = 10/31
1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/2x+1 - 1/2x+3 = 10/31
1/3 - 1/2x+3 = 10/31
1/2x+3 = 1/3 - 10/31
1/2x+3 = 1/93
`=> 2x + 3 = 93`
`=> 2x = 90`
`=> x = 45`
Vậy x = 45.
HỌC TỐT!