Question 1) If an is a decreasing and always positive sequence then lim an converges. n-+00 Question 2) Suppose lim |an converges. Then lim an...

The following questions are true or false questions. I need help proving which ones are true and which ones are false. For statements believed to be true, a proof must be provided. For statements believed to be false, a concrete counterexample must be provided.

Question 1) If an is a decreasing and always positive sequence then lim an converges.n-+00Question 2) Suppose lim |an converges. Then lim an converges.n-toon-tooQuestion 3) Every monotonic sequence converges.Question 4) Suppose an is an always increasing sequence. Then the sequence bn = 8 - 3an isan always decreasing sequence.Question 5) Suppose an is an always postive sequence and that lim an diverges.Then lim an = Co.n-toon-too