Show that the sum of a convergent and divergent series is divergent

I am completely stumped on this one, so I could really use a hand with it.

Show that if the series converges and the series diverges, then the series diverges.

A rigorous proof is expected, and we are to prove this by contradiction.

I don't know how I could answer this. This is all I really know that could possibly help me answer it.

If converges and converges, then

Moreover, if and , then

I could really use some help with this one. I wasn't able to see my Calculus professor concerning the matter due to an unexplained absence on his part.