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1/(3+6)+1/(3+6+9)+1/(3+6+9+12)+...+1/(3+6+9+...+150)=?

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/11/08 11:58:52
1/(3+6)+1/(3+6+9)+1/(3+6+9+12)+...+1/(3+6+9+...+150)=?
1/3+1/(3+6)+1/(3+6+9)+...+1/(3+6+9+...+150)
=1/3+1/[3*(1+2)]+1/[3*(1+2+3)]+...+1/[3*(1+2+3+...+50)]
=2/3*[1/(1*2)+1/(2*3)+1/(3*4)+...+1/(50*51)]
=2/3*[1-1/2+1/2-1/3+1/3-1/4+...+1/50-1/51]
=2/3*[1-1/51]
=2/3*50/51
=100/153