作业帮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``````````````````````````````11+----------+————······+——————1+2 1+2+3 1+2+3+···50
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/12 16:14:45
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``````````````````````````````11+----------+————······+——————1+2 1+2+3 1+2+3+···50
1+（1+2）分之1+（1+2+3）分之1······+（1+2+3···+50）分之1如何计算
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1+----------+————······+——————
1+2 1+2+3 1+2+3+···50
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``````````````````````````````11+----------+————······+——————1+2 1+2+3 1+2+3+···50
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
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
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。