Question

（1/2+1/3+1/4+......+1/30)+(2/3+2/4+......+2/30)+(3/4+3/5+......+3/30)+......+(28/29+28/30)+29/30

Answer 1

（1/2+1/3+1/4+.......+1/30）+（2/3+2/4+.......2/30）+（3/4+3/5+3/6+.......3/30）+......+（28/29+28/30）+29/30

=1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+……+28/30+29/30
=1/2+1+(1+1/2)+2+(2+1/2)+3+(3+1/2)+4+……+14+(14+1/2)
=1/2+(1+2+3+……+14)×2+1/2×14
=1/2+210+7
=217.5 如有疑问继续追问，谢谢采纳！

Answer 2

（1/2+1/3+1/4+.......+1/30）+（2/3+2/4+.......2/30）+（3/4+3/5+3/6+.......3/30）+......+（28/29+28/30）+29/30

=1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+……+28/30+29/30
=1/2+1+(1+1/2)+2+(2+1/2)+3+(3+1/2)+4+……+14+(14+1/2)
=1/2+(1+2+3+……+14)×2+1/2×14
=1/2+210+7
=217.5

Answer 3

（1/2+1/3+1/4+......+1/30)+(2/3+2/4+......+2/30)+(3/4+3/5+......+3/30)+......+(28/29+28/30)+29/30=1/2+(1/3+2/3)+(1/4+2/4+3/4)+…+(1/30+2/30+3/30+…+29/30)=1/2+1+(1+1/2)+2+(2+1/2)+…+(15+1/2)=(1+2+3+4+…+15)×2+15×1/2=15×16+15×1/2=247.5

Answer 4

把分母相同的加在一起。设分母为n，那么加起来是1/n+2/n+……+n-1/n=n-1/2（n不小于2）再把上式根据n加起来，得到218