for n=1a2= a1-a1lna1= a1(1-lna1) > a1a2>a1n=1 is trueAssume p(k) is trueiea(k+1) - ak >0a(k) - aklnak - ak >0aklnaka(k+1)a(k+2)-a(k+1) >0By principle of MI,it is true for all n