What is the sum from k=1 to infinity of (cos(14))^k ?

The sum from k=1 to infinity of (cos(14))^k is converges

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sum from k=1 to infinity of (cos(14))^k

k = 1 \sum \infty (cos (14))^{k}

converges

Solution steps

k = 1 \sum \infty (cos (14))^{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 (14))^{k} - (cos (14))^{0}

k = 0 \sum \infty (cos (14))^{k} =

converges

= converges - (cos (14))^{0}

= converges

n = 1 \sum \infty \frac{3}{n} - \frac{3}{n + 1}

n = 0 \sum \infty n e^{- 2 n^{2}}

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

n = 0 \sum \infty 9 (\frac{8}{9})^{n}

n = 10 \sum \infty \frac{1}{n ln ( n )}

What is the sum from k=1 to infinity of (cos(14))^k ?
The sum from k=1 to infinity of (cos(14))^k is converges