\(\sum_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\)

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Grigorios Kostakos
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\(\sum_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\)

#1

Post by Grigorios Kostakos »

Examine if the series \[\displaystyle\mathop{\sum}\limits_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\] converges.
Grigorios Kostakos
akotronis
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Re: \(\sum_{n=1}^{\infty}{(-1)^{n+1}\cos\tfrac{1}{n}}\)

#2

Post by akotronis »

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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