Convergence comparison test (sequence, calc II)

[coals]

Homework Statement

Finally done with stupid improper integrals (calc 2 over summer is hard work, moving super fast) and now I'm sequences and series and what have you. I have another comparison test problem

Instructions are to find out if sequence converges or diverges, and find limit if it converges.

Sequence is:
{A_n}= n!/(2^n) .

The Attempt at a Solution

I know what to do with the factorial most of the time. I tried expanding it but the 2^n is throwing me off because the sequence diverges. Can i get a nudge in the right direction? I don't think my instructor wants me to find the limit of it if i can avoid doing so on divergence problems (he makes a point to tell us on HW to check convergence beforehand as practice for quizzes/tests).

As always thank all of you who help out pity-able college students as myself (lol) .

 

[Dick]

You should really show us what you tried. But try a ratio test.

 

[System]

Its a sequence or a series ?
There is no comparison test for sequences.
If its a sequence: Try the sandwich theorem.
If its a series: See Dick's reply.

 

[gomunkul51]

a_(n+1) / a_(n) >= 1, so the sequence monotonic increasing.
if you can't find a limit (number) then the series goes to infinity.