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: Convergent series

  1. May 24, 2010 #1
    1. The problem statement, all variables and given/known data

    Find a sequence (an) of positive real numbers such the sum of an from 1 to infinity is convergent but the number of k such that a(k+1)>ak divided by n tends to 1 as n tends to infinity.

    2. Relevant equations

    3. The attempt at a solution
    I don't have a clue how to find a sequence here. Could anyone please give a hint? Any help is appreciated!
  2. jcsd
  3. May 24, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Be creative. Take a nice convergent decreasing series like 1/2^n. Now think about ways of rearranging the terms.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook