Sequences and Limit

[cheerio]

Hello, I'm really having a trouble with solving these three. If anyone has any suggestion or any kind of knowledge with proving I would really appreciate your help since I cant find any similar tasks anywhere online.

 

[lev888]

Please read this: https://www.freemathhelp.com/forum/threads/read-before-posting.108223/
Pick one problem.

 

[Steven G]

These problems actually are quite easy to do. Do you know your definitions?

If f(x) < M for all x, that means that f(any number) is ALWAYS less then M
Suppose that g(x) < N for all x.
You really can't figure out a upper bound for f(x) + g(x) ?? One of your questions is very similar to this.