Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Convergence comparison test (sequence, calc II)

  1. Jun 22, 2010 #1
    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. jcsd
  3. Jun 22, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    You should really show us what you tried. But try a ratio test.
  4. Jun 23, 2010 #3
    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.
  5. Jun 25, 2010 #4
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook