# Solve the inequality problem

Discussion in 'Precalculus Mathematics Homework' started by thereddevils, Jul 14, 2010.

1. Jul 14, 2010

### thereddevils

1. The problem statement, all variables and given/known data

Solve the inequality,

$$\frac{1.8^n}{n!}<0.201$$

2. Relevant equations

3. The attempt at a solution

some hints?

2. Jul 14, 2010

### lanedance

Re: inequality

have you considered Stirlings approximation for the factorial?

3. Jul 14, 2010

### lanedance

Re: inequality

for n>>1
$$n! \approx \sqrt{2 \pi n} \left( \frac{n}{e} \right)^n$$

Last edited: Jul 14, 2010
4. Jul 14, 2010

### lanedance

Re: inequality

though you'll have to check that n is pretty big... clearly n>8 here but how big...?

5. Jul 14, 2010

### thereddevils

Re: inequality

n=6, is 6 considered large?

6. Jul 14, 2010

### lanedance

Re: inequality

no sorry, i though it was 8^n...

can you just use brute force then & test n values?

7. Jul 14, 2010

### thereddevils

Re: inequality

yeah, that's how i got n=6 but i just wonder is there a tidier and definite way of solving that.
Thanks for helping me thus far.