Question

证明不等式|a+b|/1+|a+b|

Answer 1

证明：【法一】1、设 |a+b|≠0

则,|a|+|b|》|a+b|>0

所以,1/(|a|+|b|)《1/|a+b|

所以,1/(|a|+|b|)+1《1/|a+b| +1

所以,(1+|a|+|b|)/(|a|+|b|)《(1+|a+b| )/|a+b|

所以,上式倒过来得：,(|a|+|b|)/(1+|a|+|b|)》|a+b| /(1+|a+b|)

即：|a+b|/1+|a+b|