Suppose that the sequence xn has no convergent subsequences. Let M > 0. Prove that there exist at most finitely many values of n such that xn ∈ [−M, M]. Explain why this implies |xn|→[infinity] as n → [infinity].

Peter applied to an accounting firm and a consulting firm. he knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. assume that receiving an offer from one firm is independent of receiving an offer from the other. what is the probability that both firms offer peter a job?