1) Prove that if xn → ∞, then the sequence {xn/1+xn} converges. Is the converse true? Justify your answer.
2) a)Suppose {an} and {bn} are sequences of positive numbers, an → ∞, and(1) limn→∞an/bn= α for some α ∈ R. Show that bn → ∞.
(b) Given an example of sequences {an} and {bn} (whose terms need not be positive) satisfying (1) such that an → ∞ but bn /→ ±∞ (i.e. {bn} does not diverge to ∞ or -∞).