# Math Help - Maximum values of the sequence

1. ## Maximum values of the sequence

Hi
If an = (1000^n )/ n! for n=1,2,3,..... then the sequence {an} :

a. does not have a maximum
b. attains maxima at exactly one value of n
c. attains maxima at exactly two values of n
d. attains maxima for infinitely many values of n

thanks

2. Use the ratio test to show it converges, ruling out a), since if it had no maxima it would diverge.
EDIT - ignore what was here, think it was just rubbish, I cant give you a proof of why the answer is b), was getting a bit confused... Ask Mr F, he'll surely know.
Just for your info, the series reaches a maxima at n=190 then starts to converge towards 0.

3. actually the answer is C. that is why i was confused.