How do you determine if the series the converges conditionally, absolutely or diverges given $\infty \sum n = 1 \frac{cos (n π)}{n^{2}}$ $sum_(n=1)^oo (cos(npi))/n^2$ ?

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Answer 1 · 2018-02-20T09:30:14

See below.

The series

$\infty \sum k = 1 \frac{1}{k^{2}}$ $sum_(k=1)^oo 1/k^2$ converges

so

$\infty \sum k = 1 \frac{cos (k π)}{k^{2}} \leq \infty \sum k = 1 \frac{1}{k^{2}}$ $sum_(k=1)^oo cos(k pi)/k^2 le sum_(k=1)^oo 1/k^2$ converges

How do you determine if the series the converges conditionally, absolutely or diverges given sum_(n=1)^oo (cos(npi))/n^2∞∑n=1cos(nπ)n2sum_(n=1)^oo (cos(npi))/n^2?