What is the sum from k=1 to infinity of (cos(9))^k ?

The sum from k=1 to infinity of (cos(9))^k is converges

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sum from k=1 to infinity of (cos(9))^k

k = 1 \sum \infty (cos (9))^{k}

converges

Solution steps

k = 1 \sum \infty (cos (9))^{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 (9))^{k} - (cos (9))^{0}

k = 0 \sum \infty (cos (9))^{k} =

converges

= converges - (cos (9))^{0}

= converges

What is the sum from k=1 to infinity of (cos(9))^k ?
The sum from k=1 to infinity of (cos(9))^k is converges