Understanding the Cauchy-Schwarz Inequality

[Joe20]

I am not sure what examples to give, need help on this. Have attached the theorem as well.

 

[Olinguito]

You need to give an example of (i) a divergent sequence that is increasing but not bounded above, and (ii) a divergent sequence that is bounded above but not increasing. This will show that both conditions (increasing and bounded) are needed for the theorem to hold.