Nothing new is needed. Just prove that the sequence satisfies the assumptions of question 1) (with 0 as the limit).2) But now I am stuck with question 2. The assumption is replaced by (Xn)^2 ≤ W, and we need to prove more: Xn->X in mean square. I tried to modify the proof in question 1, but it doesn't seem to work here. How can we modify the proof? Or do we need something new?
Hint: using the property about subsequences, you have as well.