归纳法,数列{a(n)}满足：0

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