原式=1/(1×3)+1/(2×4)+1/(3×5)+1/(4×6)+...+1/(18×20)+1/(19×21)
=1/2［(1-1/3)+(1/2-1/4)+(1/3-1/5)+(1/4-1/6)+...+(1/18-1/20)+(1/19-1/21)］
=1/2［1+1/2-1/20-1/21］
=1/2×589/420
=589/840.