3分之1+8分之1+15分之1+24分之1+.+360分之1+399分之1=
问题描述：
3分之1+8分之1+15分之1+24分之1+.+360分之1+399分之1=
答
原式=1/(1*3)+1/(2*4)+1/(3*5)+……+1/(18*20)+1/(19*21)
=1/2*(1-1/3+1/2-1/4+1/3-1/5+……+1/18-1/20+1/19-1/21)
=1/2*(1+1/2-1/19-1/21)
不想算了，自己来
答
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.