1/(x+1)(x+2)+.+1/(x+2009)(x+2010)
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1/(x+1)(x+2)+.+1/(x+2009)(x+2010)1/(x+1)(x+2)+.+1/(x+2009)(x+2010)1/(x+1)(x+2)+.+1/(x+2009)(x+2010)1
1/(x+1)(x+2)+.+1/(x+2009)(x+2010)
1/(x+1)(x+2)+.+1/(x+2009)(x+2010)
1/(x+1)(x+2)+.+1/(x+2009)(x+2010)
1/(x+1)(x+2)+.+1/(x+2009)(x+2010)
=[1/(x+1)-1/(x+2)]+[1/(x+2)-1/(x+3)]+…+[1/(x+2009)-1/(x+2010)]
=1/(x+1)-1/(x+2010)
=2009/[(x+1)(x+2010)]
1/(x+1)(x+2)=1/(x+1) - 1/(x+2)
自己观察，看着办，另外你题目中间不确定不好说呀
=(1/x+1 - 1/x+2)+(1/x+2 - 1/x+3)+........+(1/x+2008 - 1/x+2009)+(1/x+2009 - 1/x+2010)
=1/x+1 - 1/x+2010
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