\(\sum_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\)
- Grigorios Kostakos
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\(\sum_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\)
Examine if the series \[\displaystyle\mathop{\sum}\limits_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\] converges.
Grigorios Kostakos
Re: \(\sum_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\)
Writing \(a_n=(-1)^{n+1}\cos\frac{1}{n}\) we have that \(a_{2k}\to-1\) so \(a_n\not\to0\) and consequently the series doesn't converge.
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