x/1×2 + x/2×3 + x/3×4 + ...+x/2002×2003 = 2002
x( 1/1×2 + 1/2×3 + 1/3×4 + ...+1/2002×2003 ) = 2002
x( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+1/2002 - 1/2003 ) = 2002
x(1 - 1/2003) = 2002
2002x/2003 = 2002
x = 2003