What is the sum from n=0 to infinity of (cos(pin))/n ?

The sum from n=0 to infinity of (cos(pin))/n is converges

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sum from n=0 to infinity of (cos(pin))/n

n = 0 \sum \infty \frac{cos ( πn )}{n}

converges

Solution steps

n = 1 \sum \infty \frac{cos ( πn )}{n}

Apply Alternating Series Test:

converges

= converges

k = 0 \sum \infty \frac{4 ^{k}}{k !}

j = 1 \sum \infty 3 (\frac{1}{4})^{j}

n = 1 \sum \infty \frac{n}{n + 8}

n = 9 \sum \infty \frac{1}{9 n ^{4} + 8}

n = 0 \sum \infty (0. 2^{n}) 0.7

What is the sum from n=0 to infinity of (cos(pin))/n ?
The sum from n=0 to infinity of (cos(pin))/n is converges