ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2009)(b+2009)分之1的值

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ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2009)(b+2009)分之1的值
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ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2009)(b+2009)分之1的值
ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2009)(b+2009)分之1的值

ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2009)(b+2009)分之1的值
把a=1 b=2代入到1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2009)(b+2009) 可得:
=1/1*2+1/2*3+1/3*4+1/4*5+……+1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2010-1/2011
=1-1/2011(中间项都消掉,只剩首尾两项)
=2010/2011
注:1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
1/4*5=1/4-1/5
……
1/2010*2011=1/2010-1/2011