Nustatykite eilutes konvergavima, duota lygtis

Labas vakaras, gal kas galetumete padeti isspresti 4 uzdavini?

[tex]\begin{array}{rcl} \rho & = & \lim\limits_{n \to \infty}{\frac{a_{n+1}}{a_n}} \\ & = & \lim\limits_{n \to \infty}{\frac{3^n}{(2n+1)!} \times \frac{(2n-1)!}{3^{n-1}}} \\ & = & \lim\limits_{n \to \infty}{\frac{3 \times 3^{n-1}}{(2n-1)!2n(2n+1)} \times \frac{(2n-1)!}{3^{n-1}}} \\ & = & \lim\limits_{n \to \infty}{\frac{3}{2n(2n+1)}} \\ & = & 0 \\ & < & 1 \quad \longrightarrow \quad \text{konverguoja}\end{array}[/tex]