Question

Limita sirului de la subpunctul b) ?

Answer 1

Suntem in cazul de nedeterminare ∞-∞ ,deci putem amplifica cu conjugatul.

$\displaystyle \limit\lim_{n\to\infty} (\sqrt{3n+2}-\sqrt{n+1})=\limit\lim_{n\to\infty}\dfrac{3n+2-n-1}{\sqrt{3n+2}+\sqrt{n+1}}=\\\\\limit\lim_{n\to\infty} \dfrac{2n+1}{\sqrt{3n+2}+\sqrt{n+1}}=\boxed{\infty}$