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1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+```+1/(1+2+3+```+100)＝?
题目详情
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+```+1/(1+2+3+```+100)＝?
▼优质解答
答案和解析
1/(1+2+...+n)=2/[n(n+1)]=2/n-2/(n+1)
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+```+1/(1+2+3+```+100)
=2/1-2/2+2/2-2/3+2/3-2/4+.+2/100-2/101
=2-2/101=200/101
1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+```+1/(1+2+3+```+100)
=2/1-2/2+2/2-2/3+2/3-2/4+.+2/100-2/101
=2-2/101=200/101
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