a=2,b=1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)的值如题

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a=2,b=1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)的值如题a=2,b=1,求1/ab+1/(a+1)(b+1)+1/(a+2)

a=2,b=1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)的值如题
a=2,b=1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)的值如题

a=2,b=1,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)的值如题
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008) =1/2+1/(2*3)+1/(3*4)+...+1/(2010*2009) =1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010 =1-1/2010 =2009/2010