Question

3分之1+8分之1+15分之1+24分之1+.+360分之1+399分之1=

Answer 1

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.