(1-1/2009+1/2010+1/2011) ×(1/2009+1/2010+1/2011+1/2012)-(1+1/2009+1/2010+1/2011+1/2012)×(1/2009+1/2010+1/2011)=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/29 17:07:38
(1-1/2009+1/2010+1/2011) ×(1/2009+1/2010+1/2011+1/2012)-(1+1/2009+1/2010+1/2011+1/2012)×(1/2009+1/2010+1/2011)=?

(1-1/2009+1/2010+1/2011) ×(1/2009+1/2010+1/2011+1/2012)-(1+1/2009+1/2010+1/2011+1/2012)×(1/2009+1/2010+1/2011)=?
(1-1/2009+1/2010+1/2011) ×(1/2009+1/2010+1/2011+1/2012)-(1+1/2009+1/2010+1/2011+1/2012)×(1/2009+1/2010+1/2011)=?

(1-1/2009+1/2010+1/2011) ×(1/2009+1/2010+1/2011+1/2012)-(1+1/2009+1/2010+1/2011+1/2012)×(1/2009+1/2010+1/2011)=?
原式=(1-1/2009+1/2010+1/2011)×1/2012+(1-1/2009+1/2010+1/2011-1-1/2009-1/2010-1/2011-
1/2012)×(1/2009+1/2010+1/2011)
=(2012/2011-1/2009+1/2010)×1/2012-(2/2009+1/2012)×(1/2009+1/2010+1/2011)
=1/2011-(1/2009-1/2010)×1/2012-2/(2009×2009)-1/(2009×2012)-2/(2009×2010)
-1/(2010×2012)-1/2011×(2/2009+1/2012)
=1/2011-2/(2009×2012)-1/(2009×2009)-2/(2009×2010)-1/2011×(2/2009+1/2012)
=1/2011-2/3×(1/2009-1/2012)-2/(1/2009-1/2010)-(1/2009-1/2011)-(1/2011-1/2012)
-1/(2009×2009)
=1/2011-4/3×1/2009+5/3×1/2012+2/2010-2010/2009²
=1/2011-4/6027+5/6036+1/1005-2010/2009²

令a=1/2009+1/2010+1/2011
原式=(1+a)(a+1/2010)-(1+a+1/2010)a
=(1+a)a+(1+a)*1/2010-(1+a)a-a*1/2010
=1/2010+a*1/2010-a*1/2010
=1/2010

一眼算不出来了!