a, 2/42 + 2/56 + 2/72 + ... + 2/x(x+1) =3/7
=> 2 ( 1/6.7 + 1/7.8 + 1/8.9 + ... + 1/x(x+1) ) = 3/7
ta co: 1/6.7 = (7-6) / 6.7 = 7/6.7 - 6/6.7 = 1/6 - 1/7
1/7.8 = (8-7) / 7.8 = 8/7.8 - 7/7.8 = 1/7 - 1/8
tuong tu: 1/x(x+1) = 1/x - 1/(x+1)
=> 2 ( 1/6 - 1/7 +1/7 - 1/8 + 1/8 -1/9 + ... + 1/x - 1/x+1 ) = 3/7
=> 1/6 - 1/x+1 = 3/14 => x+1/6(x+1) - 6/6(x+1) = 3/14 => x - 5 / 6(x+1) = 3/14 => x-5 = 9(x+1) / 7
=> 7( x-5 ) = 9(x+1) => 7x-35 = 9x+9 => 2x=-44 => x=-22
b, 2/1.3 + 2/3.5 + 2/5.7 +...+ 2/x(x+2) = 2.1007 / 2015 = 2014/2015
ta co: 2/1.3 = (3-1) / 1.3 = 3/1.3 - 1/1.3 = 1 - 1/3
2/3.5 = (5-3) / 3.5 = 5/3.5 - 3/3.5 = 1/3 - 1/5
tuong tu: 2/x(x+2) = 1/x - 1/(x+2)
=> 1- 1/3 +1/3 - 1/5 +1/5 - 1/7 + ... +1/x - 1/x+2 = 2014/2015
=> 1 - 1/x+2 = 2014/2015 => x+2 / x+2 - 1/x+2 = 2014/2015 => 2015 ( x+1) = 2014 (x+2)
=> 2015x + 2015 = 2014x + 4028 => x=2013