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1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)

来源:学生作业帮 编辑:灵鹊做题网作业帮 分类:数学作业 时间:2024/04/29 17:33:42
1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)
99/100
1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)
1/(1*2)+1/(1*2*3)+1/(1*2*3*4)+……+1/(1*2*3*4*……*100)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100
=1-1/100
=99/100