Question

Calculati limita sirului $x_{n}= \frac{2^n+3^n}{4^n+5^n}$. Mersi

Answer 1

x[tex] x_{n}= \frac{3^{n} (1+(2/3) ^{n} )}{5^{n} (1+(4/5) ^{n} )} \lim_{n \to \infty} ( x_{n} ) =0 \lim_{n \to \infty} ( 2/3^{n} ) =0 \lim_{n \to \infty} ( 4/5^{n} ) =0 \lim_{n \to \infty} ( 3/5^{n} ) =0 \lim_{n \to \infty} ( x_{n} ) =0 [/tex]

Answer 2

$\lim_{n \to \infty} x_n= \lim_{n \to \infty} \frac{3^n( (\frac{2}{3})^n+1) }{5^n( (\frac{4}{5})^n+1) } = \lim_{n \to \infty} (\frac{3}{5})^n* \frac{( (\frac{2}{3})^n+1) }{( (\frac{4}{5})^n+1) }=0* \frac{0+1}{0+1}= 0$