Ramirez Franklin

10/07/2023 · Escuela primaria

Exo3 : Determine the nature of the following numerical series. \( \begin{array}{llll}\text { 1) } \sum_{n \geqslant 1} \cos \left(\frac{1}{n}\right) & \text { 2) } \sum_{n \geqslant 1} \frac{1}{\sqrt{n(n+1)}} & \text { 3) } \sum_{n \geqslant 0} 5^{n} \sin \left(\frac{2}{9}\right)^{n} & \text { 4) } \frac{\sinh (n)}{\sinh (2 n)}\end{array} \) \( \begin{array}{lll}\text { 5) } \sum_{n \geqslant 0} 5^{n} \sin \left(\frac{2}{9}\right)^{n} & \text { 6) } \frac{\sinh (n)}{\sinh (2 n)} & \text { 7) } \sum_{n \geqslant 1}\left(1+\frac{x}{n}\right)^{n}, x>0\end{array} \) Hints: NCC for 1)and 7). equivalence for 2), 3) and 4). Conjugate expression in 5). Definition of sinh and equivalence in 6).