What is the sum from k=1 to infinity of (cos(17))^k ?

The sum from k=1 to infinity of (cos(17))^k is converges

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sum from k=1 to infinity of (cos(17))^k

k = 1 \sum \infty (cos (17))^{k}

converges

Solution steps

k = 1 \sum \infty (cos (17))^{k}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= k = 0 \sum \infty (cos (17))^{k} - (cos (17))^{0}

k = 0 \sum \infty (cos (17))^{k} =

converges

= converges - (cos (17))^{0}

= converges

n = 1 \sum \infty \frac{8}{1 0 ^{n}}

n = 1 \sum \infty cos (\frac{15}{n})

n = 0 \sum \infty \frac{i}{2 ^{n}}

n = 1 \sum \infty 2^{n + 1}

n = 0 \sum \infty n \cdot 2^{n}

What is the sum from k=1 to infinity of (cos(17))^k ?
The sum from k=1 to infinity of (cos(17))^k is converges