(x+1)(X+2)分之1+(X+2)(X+3)分之1+……+

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(x+1)(X+2)分之1+(X+2)(X+3)分之1+……+
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(x+1)(X+2)分之1+(X+2)(X+3)分之1+……+
(x+1)(X+2)分之1+(X+2)(X+3)分之1+……+

(x+1)(X+2)分之1+(X+2)(X+3)分之1+……+
=[(x+2)-(x+1)]/(x+1)(x+2)+1/(x+2)(x+3) +1/(x+2013)(x+2014)
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+2013)-1/(x+2014)
=1/(x+1) -1/(x+2014)
=(x+2014-x-1)/(x+1)(x+2014)
=2013/(x²+2015x+2014)