已知:n为任意实数,ab=1.求证:(aˇn/ aˇn+1)+(bˇn/ bˇn+1)=1

题目

已知:n为任意实数,ab=1.求证:(aˇn/ aˇn+1)+(bˇn/ bˇn+1)=1

答案

因为ab=1
所以a=1/b
所以a^n/(a^n+1)+b^n/(b^n+1)
=1-1/(a^n+1)+b^n/(b^n+1)
=1-1/(1/b^n +1)+b^n/(b^n+1)
=1-b^n/(b^n+1)+b^n/(b^n+1)
=1