Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

how can I show that $$\limsup_{n\to\infty} (a_n + b_n) \geq \limsup_{n\to\infty}(a_n) + \liminf_{n\to\infty}(b_n)$$

share|improve this question
    
See also this question: Properties of $\liminf$ and $\limsup$ of sum of sequences –  Martin Sleziak Mar 25 '12 at 9:08
add comment

1 Answer

up vote 4 down vote accepted

Use $\limsup_n (x_n+y_n) \le \limsup_n x_n + \limsup_n y_n$, with $x_n = a_n+b_n$ and $y_n = -b_n$.

share|improve this answer
    
Thank you very very much. –  Yuri Mar 22 '12 at 2:32
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.