prove or disprove that if a sequence does not have a converging subsequence then the sequence tend to infinity

Question

how should I approach this?

"Prove or disprove that if a sequence does not have a converging subsequence then the sequence tend to infinity or negative infinity."

Answer 1

The statement is not true.

For example the sequence $$\{(-1)^nn\}$$ does not tend to infinity and it does not have a convergent subsequence.

Try the statement for positive sequences and you may get a true proposition.