Question

I need some help with limsup. I need some help with limsup. @Mathematics

Answer 1

I'm trying to prove \(\limsup (a_{n} + b_{n}) \leq \limsup a_{n} + \limsup b_{n}\)

Answer 2

The definition I'm trying to work with is that the \(\limsup s_{n}\) is the largest \(M\) such that there are \(\infty\)ly many \(s_{n} > M - \varepsilon\) for all \(\varepsilon > 0\).

Answer 3

Be I keep coming up with if \(\alpha = \limsup a_{n}\) and \(\beta = \limsup b_{n}\), then there are \(\infty\)ly many \(a_{n} > \alpha - \varepsilon\) and \(\infty\)ly many \(b_{n} > \beta - \varepsilon\)

Answer 4

Figured out my problem. The \(n\) don't have to be the same. Thanks for listening!