Question

$Sa~se~det.~parametrul~a:\\ \\ \lim_{n \to \infty} \{ a\sqrt{n+2}+(a^2+a-3) \sqrt{n} \}=0$

Answer 1

$\lim_{n \to \infty}{\sqrt{n}( a^{2}+(1+\sqrt{1+\frac{2}{n} })a-3)}=0$

Ca limita asta sa tinda la 0 e nevoie ca ce e intre paranteze "(...)" sa tinda la zero, daca ar tinde spre altceva limita ar fi + sau - infinit.

$lim_{n \to \infty}( a^{2}+(1+\sqrt{1+\frac{2}{n} })a-3)= a^{2}+2a-3=0$

Delta=16 deci a1=1 si a2=-3

S={-3,1}