ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2008)(b+2008)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+2008)(b+2008)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+2008)(b+2008)分之1的值
ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2008)(b+2008)分之1的值

ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2008)(b+2008)分之1的值
a=1 ,b=2时,求ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2008)(b+2008)分之1的值
ab分之1+(a+1)(b+1)分之1+(a+2)(b+2)分之1+……+(a+2008)(b+2008)分之1
=1/(1x2)+1/(2x3)+1/(3x4)+……+1/(2009x2010)
=1-1/2+1/2-1/3+1/3-1/4+……+1/2009-1/2010
=1-1/2010
=2009/2010