Is my proof of this sequence's divergence good enough?

[mathnoobie]

Ʃ n=1 to infinity of cos(n∏)
letting an=cos(n∏), I rewrote this as (-1)^n=an.

Using the nth term test i let the limit as n->∞ go to infinity. This value bounces back and forth between positive and negative, but I know clearly the value =/= 0, therefore it diverges by the nth term test.

Is there anything I should add to my proof?

 

[DonAntonio]

Ʃ n=1 to infinity of cos(n∏)
letting an=cos(n∏), I rewrote this as (-1)^n=an.

Using the nth term test i let the limit as n->∞ go to infinity. This value bounces back and forth between positive and negative, but I know clearly the value =/= 0, therefore it diverges by the nth term test.

Is there anything I should add to my proof?

Looks fine to me, although with a somewhat folkloric language as "bouncing back and forth" and "n-th term test", which I don't what

is. Perhaps you meant simply that the series doesn't converge as its general element's sequence doesn't converge to zero, which is a necessary condition.

DonAntonio