Question

Sa se studieze convergenta seriilor

Answer 1

$\sum\limits_{n=0}^{\infty} \dfrac{1}{5^n+3^n}\leq \sum\limits_{n=0}^{\infty} \dfrac{1}{5^n} = \sum\limits_{n=0}^{\infty}\Big(\dfrac{1}{5}\Big)^n\\ \\ |r|= \Big|\dfrac{1}{5}\Big|<1 \Rightarrow \text{converge}$