Let (sn) be a real sequence and s in R. Prove that lim sup (sn) < s implies(adsbygoogle = window.adsbygoogle || []).push({});

sn < s for n large.

My answer seems too easy. Is there anything missing?

Given lim sup (sn) < s.

By definition of lim sup, we know lim N->infinity sup {sn: n > N} < s

Then for n > N, we must have sn < s.

Colleen

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

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: Test Review 4 - is it this easy?

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