Ok.. Here's a list of a few more stuff I want to clarify:
Q33. FALSE. Can I have a counterexample? Because I thought the restriction of a_n being positive decreasing and null makes it true?
Q45. FALSE. I think False is right but your counterexample is not a correct counterexample because a_n tends to 1? I think we are looking for a_n that does not converge. My counterexample is a_n=(n-2)^2. Since there exists an N=2 s.t. abs(a_2-0)=0<epsilon for all epsilon>0, but a_n does not tend to 0.
Q67. I know that it's out of syllabus, but just for discussion sake, doesn't the example a_n=10+(1/n) show that it's false?
thats abt it. anyways, thx for putting up e solns!