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].

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.