N.1.- \[\sum_{n=1}^{+\infty }ln\left ( \frac{n^{\alpha \beta }+1}{n^{\alpha }+n^{\beta }+2} \right ),\, \, \, \, \alpha ,\beta >0\]
N.2.- \[\sum_{n=1}^{+\infty }\frac{ln\left ( \frac{n^{2}}{n^{4}-2} \right )cos\left ( \frac{n^{2}\pi }{n+1} \right )}{\sqrt{n^{2}+3}}\]
N.3.- \[\sum_{n=1}^{+\infty }\frac{sen\left ( \frac{n+1}{n^{2}+2} \right )}{ln^{2}\left ( n+3 \right )}\]
N.4.- \[\sum_{n=1}^{+\infty }\frac{cos\left ( \frac{n+2}{n^{2}+3} \right )}{ln\left ( n! \right )\cdot ln\left ( \frac{n^{2}+3}{n+2} \right )}\]
N.5.- \[\sum_{n=1}^{+\infty }\frac{sen\left ( \frac{2n}{n^{2}+1} \right )}{ln\left ( 1+\frac{n}{n^{2}+1} \right )}\]
N.6.- \[\sum_{n=1}^{+\infty }\frac{ln\left ( \frac{n^{\alpha }}{n+2} \right )}{nln^{3}\left ( n+2 \right )},\, \, \alpha \in R\]
N.7.- \[\sum_{n=1}^{+\infty }\frac{sen\left ( \frac{n\pi }{2} \right )arctan^{\beta }\left ( \frac{n}{n^{2}+1} \right )}{ln^{\alpha }\left ( n+1 \right )},\, \, \alpha ,\beta \in R\]
N.8.- \[\sum_{n=1}^{+\infty }\frac{sen\left ( \frac{n^{2}\pi }{3n+1} \right )}{ln\left ( \frac{n^{2}\pi }{3n+1} \right )}\]
N.9.- \[\sum_{n=1}^{+\infty }\frac{sen\left ( \frac{2n}{n^{2}+1} \right )}{n^{\beta }ln\left ( n^{\alpha }+1 \right ) },\, \, \alpha ,\beta >0\]