# Convergence comparison test (sequence, calc II)

1. Jun 22, 2010

### coals

1. The problem statement, all variables and given/known data
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:
{An}= n!/(2^n) .

3. 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 becuase 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) .

2. Jun 22, 2010

### Dick

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

3. Jun 23, 2010

### 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.

4. Jun 25, 2010

### 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.