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: Prove that the lim of the sequence (S_n)=0

  1. Oct 6, 2012 #1
    1. The problem statement, all variables and given/known data
    suppose that (s_n) and (t_n) are sequences in which abs(s_n)≤t_n for all n and let lim(t_n)=0. Prove that lim (s_n)=0.

    3. The attempt at a solution
    I find absolute values to be really sketchy to work with I'm really in the dark if this is at all correct:

    Let ε>0 be given, then -ε<(t_n)<ε for some n>N since the limit exists. Since -t_n≤ s_n ≤ t_n for all we can say that for -ε<-t_n≤ S_n≤t_n<ε for n>N above. hence lim(S_n)=0.

    If you have any suggestion about how to deal with the absolutes in a general manner in these kind of proofs I'd be happy to hear it.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 6, 2012 #2


    User Avatar
    Homework Helper

    Ahh now there's a very nice trick you can apply here. Recall the squeeze theorem works the same way it does for functions as it does for sequences.

    So :

    |sn| ≤ tn

    Tells us that :

    -tn ≤ sn ≤ tn
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook