anonymous
  • anonymous
Show that if a_n >0 and summation of a_n is convergent, then summation of ln(1+a_n) is convergent
Mathematics
schrodinger
  • schrodinger
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nowhereman
  • nowhereman
Use the majorizing criteria.
dumbcow
  • dumbcow
If sum of a_n converges, then lim a_n =0.(as n goes to infinity) If lim a_n =0, then lim ln(1+a_n)=0. If lim ln(1+a_n)=0, then sum of ln(1+a_n) converges.
nowhereman
  • nowhereman
That is not true. Just knowing that the elements of the series converge to 0 does not mean that the series converges. Take 1/n for example where the series diverges.

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dumbcow
  • dumbcow
ok thanks i wasn't sure if my reasoning was correct there. What would be the correct reasoning for showing this? you could show that ln(1+a_n) <= a_n for all n>=0
nowhereman
  • nowhereman
yes, that is true.
dumbcow
  • dumbcow
thanks
anonymous
  • anonymous
sevenlash, did you get this problem sorted? If not, let me know. I looked at it and have a solution.
anonymous
  • anonymous
Just not much point writing it out unless you need it :)

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