Question

已知A=2007/2008=2008/2007,B=2006/2005+2005/2006.那么,A和B相比哪个大?

Answer 1

解：∵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

Answer 2

A=2007/2008+2008/2007=1-1/2008+1+1/2007=2+(1/2007-1/2008)=2+1/(2007*2008)
B=2006/2005+2005/2006=1+1/2005+1-1/2006=2+(1/2005-1/2006)=2+1/(2005*2006)
2005*2006<2007*2008
所以A<B