exo7 4565

$a_n \to \ell \ne 0$ lorsque $n\to\infty$

$(a_n)$ est périodique non nulle.

$a_n = \sum_{d\mid n} d^2$.

$a_n = \frac{n^n}{n!}$.

$a_{2n} = a^n$, $a_{2n+1} = b^n$,

$0<a<b$.

$a_{n^2} = n!$, $a_k = 0$ si $\sqrt k \notin\N$.

$a_n = (\ln n)^{-\ln n}$.

$a_n = e^{\sqrt n}$.

$a_n = \frac{1.4.7\dots(3n-2)}{n!}$.

$a_n = \frac1{\sqrt n^{\sqrt n}}$.

$a_n = \left(1+\frac12+\dots+\frac1n\right)^{\ln n}$.

$a_{n+2} = 2a_{n+1} + a_n$,

$a_0=a_1=1$.

$a_n = C_{kn}^n$.

$a_n = e^{(n+1)^2} - e^{(n-1)^2}$.

$a_n = \int_{t=0}^1 (1+t^2)^n\,d t$.

$a_n=\sqrt[n]n-\sqrt[{n+1}]{n+1}$.

$a_n=\frac{\cos n\theta}{\sqrt n+(-1)^n}$.