X/1×2 + X/2×3 + X/3×4+ ... + X/2001×2002 = 2001
X(1/1×2 + 1/2×3 + 1/3×4+ ... + 1/2001×2002) = 2001
X(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2001 - 1/2002 ) = 2001
X(1 - 1/2002) = 2001
2001X/2002 = 2001
X = 2002