What is the sum from n=1 to infinity of (cos(pin))/n ?

The sum from n=1 to infinity of (cos(pin))/n is converges

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sum from n=1 to infinity of (cos(pin))/n

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

converges

Solution steps

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

Apply Alternating Series Test:

converges

= converges

n = 1 \sum \infty \frac{1}{7 n}

n = 1 \sum \infty (\frac{5}{4})^{n - 1}

n = 1 \sum \infty \frac{1}{4 ^{n} - 1}

n = 1 \sum \infty (1 + \frac{2}{n})^{n}

n = 1 \sum \infty 3^{\frac{1}{n}}

What is the sum from n=1 to infinity of (cos(pin))/n ?
The sum from n=1 to infinity of (cos(pin))/n is converges