# Sequence

• March 30th 2010, 02:24 AM
lehder
Sequence
Hi,

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

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

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

Can you help me please???

Thanks.
• March 30th 2010, 02:46 AM
tonio
Quote:

Originally Posted by lehder
Hi,

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

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

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

Can you help me please???

Thanks.

!!! The deduction is only the very application of the definition of limit!! For example, take $\epsilon=\frac{1}{8}$ ...

Tonio