Hi,

$\displaystyle (\forall n \in \mathbb{N})\ \ U_n=\frac{n^2}{2^n}$

I should calculate $\displaystyle \lim_{n\to +\infty} \frac{U_{n+1}}{U_n}$

and I must deduct that there is a $\displaystyle n_0$ in $\displaystyle \mathbb{N}$ such as :$\displaystyle (\forall n \ge n_0) \ \frac{U_{n+1}}{U_n} < \frac{3}{4}.$

For the limit, it's equal to $\displaystyle \frac{1}{2}$, but for the deduction, idon't know anything.

Can you help me please???

Thanks.