Question

Exercițiile 10 și 11, va rog! Coroana :D

Answer 1

10) $\lim_{n \to \infty} \frac{2n-3}{n^2+2n-2}= \lim_{n \to \infty} \frac{n(2- \frac{3}{n}) }{n^2(1+ \frac{2}{n}- \frac{2}{n^2}) }= \frac{2-0}{infinit}=0$
11)$\lim_{n \to \infty} \frac{5+5^2+...+5^n}{5^n-2}= \lim_{n \to \infty} \frac{5 \frac{5^n-1}{5-1} }{5^n-2}= \frac{5}{4} \lim_{n \to \infty} \frac{5^n(1- \frac{1}{5^n}) }{5^n(1- \frac{2}{5^n}) }= \frac{5}{4} \frac{1}{1}= \frac{5}{4}$