I am currently in an intro to real analysis class, and we are on limits now. The last time I had to deal with limits was in my last calculus class two years ago. So I am very rusty when it comes to limits. Any help, hints, suggestions, and/or corrections is greatly appreciated. Thank you for your time!

(A) Give an example of a bounded sequence that diverges.

* In class we already had the example of the sequence . Since it keeps bouncing back and forth.

I was thinking maybe a sequence dealing with a trig function say sin x or cos x maybe?

I'm stuck on B and C.

(B) Give an example of a sequence of positive real numbers, { }, where { } converges and .

(C) Give an example of a sequence of positive real numbers, { }, such that but { } diverges.