如题所述
1*1/2+2*1/3+3*1/4+......+2010*1/2011
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/2010-1/2011)
=1-1/2+1/2-1/3+1/3-1/4+......1/2010-1/2011
=1-1/2011
=2010/2011
打字累死了,多给点分吧
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+......+(1/2010-1/2011)
=1-1/2+1/2-1/3+1/3-1/4+......1/2010-1/2011
=1-1/2011
=2010/2011
打字累死了,多给点分吧
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第1个回答 2011-09-05
1/n(n+1)=1/n-1/(n+1)
1/1×2+1/2×3+.....+1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+...1/2009-1/2010.+1/2010-1/2011
=1-1/2011
=2010/2011
1/1×2+1/2×3+.....+1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+...1/2009-1/2010.+1/2010-1/2011
=1-1/2011
=2010/2011
第2个回答 2011-09-05
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(2010*2011)
=(1-1/2)+ (1/2-1/3)+ (1/3-1/4)+……+(1/2010-1/2011)
=1-1/2011
=2010/2011本回答被提问者采纳
=(1-1/2)+ (1/2-1/3)+ (1/3-1/4)+……+(1/2010-1/2011)
=1-1/2011
=2010/2011本回答被提问者采纳