How do I know if this discrete-time system is stable?

1. Oct 3, 2011

interxavier

1. The problem statement, all variables and given/known data
Given the following system:

$$s[n] = (\frac{1}{4})^{n}u[n+10]u[n]$$

Prove if this is a stable or unstable system.

2. Relevant equations

3. The attempt at a solution

I know that in order for a system to be stable, the input must be bounded in order for the output to be bounded. For example,

$$x[n] \leq B_{x}$$
$$y[n] \leq B_{y}$$
$$So, y[n] = \sum_{k = 0}^{\infty}x[n]h[n]$$
$$y[n] = \sum_{k = 0}^{\infty}B_{x}h[n] = B_{y}$$

Last edited: Oct 3, 2011