Question

Describe all the positive integers that would make [1/2^4]^n less than (1/2). Explain your reasoning

Answer 1

We have the following inequation:

$\begin{gathered} (\frac{1}{2^4})^n<\frac{1}{2} \\ \frac{1}{2^{(4\cdot n)}}<\frac{1}{2} \\ 2^{4n}>2 \\ \end{gathered}$

The values of n that satisfy the inequation are such that 4n > 1, so:

$\begin{gathered} 4n>1 \\ n>\frac{1}{4} \end{gathered}$

But n is an integer, so any positive integer satisfy the inequation