Determine whether the series is convergent or divergent.

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SUMMARY

The series in question is \(\Sigma (-1)^n \cdot \cos(\pi/n)\) from n=1 to infinity. The limit of the absolute value of the function as n approaches infinity is 1, indicating that the terms do not approach zero. According to the Alternating Series Test, for a series to converge, the limit of the terms must approach zero, which is not the case here. Therefore, the series is divergent as confirmed by the textbook.

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  • Basic knowledge of limits in calculus
  • Knowledge of trigonometric functions, specifically cosine
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Hello,

I have to determine whether the series converges or diverges.

It is \Sigma (-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 textbook says it's divergent. Could you please help me understand why it is divergent?

Thank you!
 
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Nevermind! I figured out why. I guess I confused the alternating series test with some other one. :)

Thanks!
 

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