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I have to determine whether the series converges or diverges.

It is [tex]\Sigma[/tex] (-1)^n * cos(Pi/n) where n=1 and goes to infinity.

First I took the absolute value of the function and got the limit from n to infinity of cos(pi/n) and as a result I got 1 because cos(0)=1. However my text book says it's divergent. Could you please help me understand why it is divergent?

Thank you!