Răspuns:
[tex]\frac{e^{n^2}-e^n}{n-1}\geq en[/tex] <=> [tex] e^{n^2}-e^n\geq en(n-1)=en^2-en[/tex] <=> [tex] e^{n^2}-en^2 \geq e^n-en [/tex] <=> [tex] e^{n^2}-en^2-1 \geq e^n - en -1 [/tex] <=> [tex] f(n)\geq f(\sqrt n) [/tex] (adevarat, pentru ca [tex]n>\sqrt n > 1[/tex] si f e crescatoare pe [tex][1,\infty)[/tex].
