1+（1+2）分之1+（1+2+3）分之1······+（1+2+3···+50）分之1如何计算
问题描述：
1+（1+2）分之1+（1+2+3）分之1······+（1+2+3···+50）分之1如何计算
```````1```````````1``````````````````````````````1
1+----------+————······+——————
1+2 1+2+3 1+2+3+···50
答
1+2+……+n=n(n+1)/2
所以1+1/(1+2)+1/(1+2+3)+……+1/(1+2+……+50)=1+2/(2×3)+2/(3×4)+……+2/(50×51)=2/(1×2)+2/(2×3)+2/(3×4)+……+2/(50×51)=2×(1/(1×2)+1/(2×3)+1/(3×4)+……+1/(50×51))=2×(1-1/2+1/2-1/3+1/3-1/4+……+1/50-1/51)=2×50/51=100/51