Can I use the divergence test on the partial sum of the telescoping series?(adsbygoogle = window.adsbygoogle || []).push({});

Lim n>infinity an if not equal zero then it diverges

The example below shows a telescoping series then I found the partial sum and took the limit of it. My question is shouldn't the solution be divergent? Since the result -1+cos 1 is not equal to 0? I'm confused.

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# I Divergence/Convergence for Telescoping series

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