六分之一+十二分之一+二十分之一+三十分之一…+2005×2006分之1
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六分之一+十二分之一+二十分之一+三十分之一…+2005×2006分之1
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+……+1/(2005×2006)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)……+(1/2005-1/2006)
=1/2-(1/3-1/3)-(1/4-1/4)-(1/5-1/5)-(1/6-1/6)……-(1/2005-1/2005)-1/2006
=1/2-1/2006
1003/2006-1/2006
=1002/2006
=501/1003
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+……+1/(2005×2006)
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)……+(1/2005-1/2006)
=1/2-(1/3-1/3)-(1/4-1/4)-(1/5-1/5)-(1/6-1/6)……-(1/2005-1/2005)-1/2006
=1/2-1/2006
1003/2006-1/2006
=1002/2006
=501/1003
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