Question

Calculati limita sirului:
$\lim_{n \to \infty} \frac{1+2^{2n+1} }{3*2^{2n+1} }$

Answer 1

Salut,

Avem succesiv că:

$\lim\limits_{n\to+\infty}\dfrac{1+2^{2n+1}}{3\cdot 2^{2n+1}}=\lim\limits_{n\to+\infty}\dfrac{1}{3\cdot 2^{2n+1}}+\lim\limits_{n\to+\infty}\dfrac{2^{2n+1}}{3\cdot 2^{2n+1}}=\dfrac{1}{3\cdot\infty}+\lim\limits_{n\to+\infty}\dfrac{1}{3}=\\\\\\=0+\dfrac{1}3=\dfrac{1}3.$

Ai înțeles rezolvarea ?

Green eyes.