1/3 + 1/6 + 1/10 + ... + 2/x(x + 1) = 1999/2001
2 × (1/6 + 1/12 + 1/20 + ... + 1/x(x + 1) = 1999/2001
1/2×3 + 1/3×4 + 1/4×5 + ... + 1/x(x + 1) = 1999/2001 : 2
1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/x - 1/x+1 = 1999/2001 × 1/2
1/2 - 1/x+1 = 1999/4002
1/x+1 = 1/2 - 1999/4002
1/x+1 = 2/4002 = 1/2001
=> x + 1 = 2001
=> x = 2001 - 1 = 2000
Vậy x = 2000