It's simple to see that the SEQUENCE converges to 1. eg. .

The nth term test is used to test whether a SERIES, not a sequence, diverges!! And clearly the series diverges (the sum of 1's --> oo). Unsurprising since the nth term does not approach zero.

Or are you asking for a proof of the nth term (limit) test? If so, consult any standard reference on the topic .....