1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/27 13:14:40
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200)=?
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1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200)=?
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200)=?

1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200)=?
1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+······+1/(1+2+3+······+200) =1/3+1/6+1/10+.+1/[(1+200)*200/2] =1/3+1/6+1/10+.+1/20100 =2(1/6+1/12+1/20+.+1/40200) =2(1/2-1/3+1/3-1/4+1/4-1/5+.+1/200-1/201) =2×(1/2--1/201) =1-2/201 =199/201