Question

S3,ex1 c)
Va rog mult!:)))

Answer 1

Răspuns:

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