Homework Help: Cant understand how they use a theorem question

1. Mar 12, 2009

transgalactic

i marked a place where they use theorem 4

but theorem 4 talks about that if one sequence is bigger then the other
then so is their liminf and limsup
it doesnt tell anything about the limsup of the sum of the sequences

i cant understand how they use this fact for getting the marked result
what does theorem 4 has to do with the limsup of the sum of sequences
??

Last edited: Mar 13, 2009
2. Mar 12, 2009

wywong

Let $$\alpha_n = a_n+b_n,\ \beta_n = a+b+\epsilon$$(constant) and apply theorem 4 for the sequences $$\alpha_n$$ and $$\beta_n$$ and you will get the result.

3. Mar 12, 2009

transgalactic

i cant see how i get the supreme of the sum of both sequences
using theorem 4

??

4. Mar 12, 2009

transgalactic

theorem 4 talks about that if one sequence is bigger then the other
then so is the liminf of the first is bigger then the other and so is for limsup
it doesnt tell anything about the limsup of the sum of the sequences
??

5. Mar 13, 2009

transgalactic

i cant understand what you are saying
how ill get the result
/??

6. Mar 13, 2009

transgalactic

why a_n +b_n =limsup(a_n +b_n)
??