计算:2/(x+1)(x+3)+2/(x+3)(x+5)……+2/(x+2013)(x+2015
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2/[(x+1)(x+3)]+2/[(x+3)(x+5)]+……+2/[(x+2013)(x+2015)]
=[1/(x+1)-1/(x+3)]+[1/(x+3)-1/(x+5)]+……+[1/(x+2013)-1/(x+2015)]
=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+……+1/(x+2013)-1/(x+2015)
=1/(x+1)-1/(x+2015)
=[(x+2015)-(x+1)]/[(x+1)(x+2015)]
=2014/[(x+1)(x+2015)]
=[1/(x+1)-1/(x+3)]+[1/(x+3)-1/(x+5)]+……+[1/(x+2013)-1/(x+2015)]
=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+……+1/(x+2013)-1/(x+2015)
=1/(x+1)-1/(x+2015)
=[(x+2015)-(x+1)]/[(x+1)(x+2015)]
=2014/[(x+1)(x+2015)]
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