What is the sum from k=1 to infinity of (cos(6))^k ?

The sum from k=1 to infinity of (cos(6))^k is converges

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sum from k=1 to infinity of (cos(6))^k

k = 1 \sum \infty (cos (6))^{k}

converges

Solution steps

k = 1 \sum \infty (cos (6))^{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 (6))^{k} - (cos (6))^{0}

k = 0 \sum \infty (cos (6))^{k} =

converges

= converges - (cos (6))^{0}

= converges

n = 1 \sum \infty \frac{n !}{8 6 ^{n}}

n = 2 \sum \infty \frac{n}{ln ( 9 n )}

k = 1 \sum \infty k (\frac{7}{8})^{k}

n = 1 \sum \infty \frac{5}{2 n ^{2}}

n = 1 \sum \infty 7 - 2 (0.9)^{n}

What is the sum from k=1 to infinity of (cos(6))^k ?
The sum from k=1 to infinity of (cos(6))^k is converges