已知A=2007/2008=2008/2007,B=2006/2005+2005/2006.那么,A和B相比哪个大?
问题描述:
已知A=2007/2008=2008/2007,B=2006/2005+2005/2006.那么,A和B相比哪个大?
答
∵A=2007/2008+2008/2007∴A=1-1/2008+1+1/2007=2+(1/2007-1/2008)=
2+1/2007×2008
∵B=2006/2005+2005/2006∴B=1+1/2005+1-1/2006=2+(1/2005-1/2006)=
2+1/2005×2006
∵1/2007×2008<1/2005×2006,∴ 2+1/2007×2008<2+1/2005×2006∴ A<B