Question

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

Answer 1

楼主你好
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
希望你满意

Answer 2

sunnyandi的回答非常好啊，可能还不太明白，第三步后，1/（1×2)＝1/1-1/2,
1/(2×3)1/2-1/3……以此类推，最后括号里，仅剩下1-1/51，最终结果就是2*50/51＝100/51,这个方法很不错。

Answer 3

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
希望你满意