Exo3 : Determine the nature of the following numerical series. $$ \begin{array}{llll} ext { 1) } \sum_{n \geqslant 1} \cos \left(\frac{1}{n} ight) & ext { 2) } \sum_{n \geqslant 1} \frac{1}{\sqrt{n(n+1)}} & ext { 3) } \sum_{n \geqslant 0} 5^{n} \sin \left(\frac{2}{9} ight)^{n} & ext { 4) } \frac{\sinh (n)}{\sinh (2 n)} \ ext { 5) } \sum_{n \geqslant 0} 5^{n} \sin \left(\frac{2}{9} ight)^{n} & ext { 6) } \frac{\sinh (n)}{\sinh (2 n)} & ext { 7) } \sum_{n \geqslant 1}\left(1+\frac{x}{n} ight)^{n}, x0\end{array} $$

Question

Exo3 : Determine the nature of the following numerical series. $$ \begin{array}{llll}	ext { 1) } \sum_{n \geqslant 1} \cos \left(\frac{1}{n}ight) & 	ext { 2) } \sum_{n \geqslant 1} \frac{1}{\sqrt{n(n+1)}} & 	ext { 3) } \sum_{n \geqslant 0} 5^{n} \sin \left(\frac{2}{9}ight)^{n} & 	ext { 4) } \frac{\sinh (n)}{\sinh (2 n)} \ 	ext { 5) } \sum_{n \geqslant 0} 5^{n} \sin \left(\frac{2}{9}ight)^{n} & 	ext { 6) } \frac{\sinh (n)}{\sinh (2 n)} & 	ext { 7) } \sum_{n \geqslant 1}\left(1+\frac{x}{n}ight)^{n}, x>0\end{array} $$

Perkins Watkins · Accepted Answer

1) Diverges 2) Diverges 3) Diverges 4) Converges 5) Diverges 6) Converges 7) Diverges

Solución ThothAI de Upstudy

Respuesta rápida

Solución paso a paso

Solución ThothAI de Upstudy

Respuesta rápida

Solución paso a paso

preguntas relacionadas