1/2+5/6+11/12+19/20+29/30+...+109/110
=1-1/2+1-1/6+1-1/12+1-1/20+1-/30+...+1-1/110
=10-(1/2 +1/6+1/12+1/20+1/30+..+1/110)
=10-(1/(1*2) +1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+..+1/(10*11))
=10-(1-1/2 +1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+..+1/10-1/11)
=10-(1-1/11)
=9+1/11
=9å1/11
=1-1/2+1-1/6+1-1/12+1-1/20+1-/30+...+1-1/110
=10-(1/2 +1/6+1/12+1/20+1/30+..+1/110)
=10-(1/(1*2) +1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+..+1/(10*11))
=10-(1-1/2 +1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+..+1/10-1/11)
=10-(1-1/11)
=9+1/11
=9å1/11
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第1个回答 2014-11-02
(1-1/2)+(1-1/6)+(1-1/12)+(1-1/20)+(1-1/30)+...+(1-1/110)
=10-(1/2+1/6+1/12+1/30++...+ 1/110 )
=10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6......+1/10-1/11)
=10-(1-1/11)
=9+10/11
=10-(1/2+1/6+1/12+1/30++...+ 1/110 )
=10-(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6......+1/10-1/11)
=10-(1-1/11)
=9+10/11
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