Ta có: 1/1x2 + 1/2x3 + 1/3x4 +...+ 1/X x (X + 1) = 499/500
=> 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +...+ 1/X - 1/(X + 1) = 499/500
=> 1 - 1/(X + 1) = 499/500
=> 1/(X + 1) = 1 - 499/500
=> 1/(X + 1) = 1/500
=> X + 1 = 500
=> X = 500 - 1
=> X = 499
Đáp số: X = 499