Determine if a series converges, cosine, Taylor

by Jon Lachmann   Last Updated September 11, 2019 13:20 PM

How do I determine if the series $$ \sum_{k=1}^{\infty} 1- \cos \frac{1}{k} $$ converges?

I got a hint that I should use Taylor expansion, but I cant figure out how it would be applied correctly here.

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