Use the divergence test to determine if the following series MUST diverge.
If we write out the nth term of this series we get
The n and 2 cancel from the numerator and the denominator. This leaves us with an expression that has 2 on the bottom and (n – 1) multiplied by a lot of stuff in the top:
As n approaches ∞, the terms given by this expression will also approach infinity. Thus the series diverges.