How can the inequality problem be solved for 1.8^n/n! < 0.201?

[thereddevils]

Homework Statement

Solve the inequality,

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

Homework Equations

The Attempt at a Solution

some hints?

 

[lanedance]

have you considered Stirlings approximation for the factorial?

 

[lanedance]

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

 

[lanedance]

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

 

[thereddevils]

n=6, is 6 considered large?

 

[lanedance]

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

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

 

[thereddevils]

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

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

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.