1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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: Find a_n & b_n such that

  1. Dec 22, 2014 #1
    1. The problem statement, all variables and given/known data
    Find [tex]a_n[/tex] & [tex]b_n[/tex] such that [tex]\sum_{n=0}^{\infty}a_n[/tex] & [tex]\sum_{n=0}^{\infty}b_n[/tex] are convergent series, but [tex]\displaystyle \sum_{n=0}^{\infty} \left( \sqrt{a_n} \cdot b_n \right)[/tex] diverges.

    2. Relevant equations

    3. The attempt at a solution
    Try too hard for this but still cannot find such [tex]a_n[/tex] & [tex]b_n[/tex].
  2. jcsd
  3. Dec 22, 2014 #2


    User Avatar

    Staff: Mentor

    That is not an acceptable post. You must show your efforts before we can offer tutorial help. Show us what you have tried so far please...
  4. Dec 22, 2014 #3
    There is nothing to show here
    basically I tried a_n = 1/n^2 & b_n = (-1)^n / n but failed
    tried a_n = 1/n^2 & b_n = arctan (1/n) but failed
    and so on...
  5. Dec 22, 2014 #4


    User Avatar
    2017 Award

    Staff: Mentor

    That is not so bad as a start. Can you modify the series in order to keep them converging, but doing so significantly slower?
    And then you'll need some trick to get the product diverging - something that changes the sign flip thing...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted