Another divergence proof: Prove 1/a_n converges to ∞ (i.e. 1/a_n diverges).

If > 0 n and = 0, prove that .

I haven't been able to write up a proof for this one yet. I have a few ideas down:

Since { } 0, by definition of convergence, I know | | < , or

- < < .

Starting ideas for proof:

Assume = 0 and > 0 n .

{ } 0 | - 0| < | | < | | > , since > 0 .....

I was working with my classmates, and we were guessing that we would reach a contradiction somehow using the definition of convergence, and then by ______ (we don't know what exatly) we will conclude that the sequence has to diverge by contradiction to our assumption.

Any help, suggestions, tips, corrections, guidance, etc. is greatly appreciated. Thank you very much for looking and for your time! (Nod)