已知a=2,b=1且1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)的值.

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已知a=2,b=1且1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)的值.
已知a=2,b=1且1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)的值.

已知a=2,b=1且1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)的值.
已知a=2,b=1且1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)的值.
1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2011)(b+2011)
=1/3*2+1/4*3+1/5*4+.+1/2013*2012
=1/2-1/3+1/3-1/4+1/4-1/5+.-1/2012+1/2012-1/2013
=1/2-1/2013
=(2013-2)/4026
=2011/4026