∵1/n(n-1)=[n-(n-1)]/n(n-1)=1/(n-1)-1/n
∴1/(1*2)=1/1-1/2; 1/(2*3)=1/2-1/3.
原式=1/（1*2）+1/（2*3）+1/(3*4)+1/(4*5)+.+1/（10*11）
=1/1-1/2+1/2-1/3+1/3-1/4+.+1/10-1/11
=1-1/11
=10/11
1／2＋1／6＋1／12＋1／20＋1／30＋1／42＋1／56＋1／72＋1／90＋1／110＝?
5个回答
相关问题
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计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110=?
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计算1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110=?
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1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90+1/110 +······1/99
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1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+190+1/110=?
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2\1-6\1-12\1-20\1-30\1-42\1-56\1-72\1-90\1
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1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=
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2/1＋6/1＋12/1＋20/1＋30/1＋42/1＋56/1＋72/1＋90/1
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1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
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1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90=?
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2\1+6\1+12\1+30\1+42\1+56\1+72\1+90\1+110\1= (提示：2\1=1-2\1.6