Given #a in RR^+, a ne 1# and #n in NN, n > 1# Prove that #n^2 < (a^n + a^(-n)-2)/(a+a^(-1)-2)#?
2 Answers
Let a > 1. Then
, using
Likewise, when a < 1,
, using
So, the given expression is
then
with
This is a continuous even function having a minimum at
also we have
so the proof follows.