[tex](adsbygoogle = window.adsbygoogle || []).push({});

\liminf _{n->\infty} x_n+\limsup _{n->\infty} y_n\leq \limsup _{n->\infty} (x_n+y_n)\leq\limsup _{n->\infty} x_n+\limsup _{n->\infty} y_n\\

[/tex]

proving the first part:

[tex]

\limsup _{n->\infty} (x_n+y_n)\leq\limsup _{n->\infty} x_n+\limsup _{n->\infty} y_n\\

[/tex]

lim sup is the supremum of all the limits of the subsequences

this is true because of some law regarding the sum of two subsequences

correct??

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Lim inf/sup innequality question

**Physics Forums | Science Articles, Homework Help, Discussion**