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

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

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

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

converges

Solution steps

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

Simplify

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

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^{k} (1) - cos^{0} (1)

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

converges

= converges - cos^{0} (1)

= converges

n = 3 \sum \infty \frac{2 n}{n + 2}

k = 2 \sum \infty (- 0.65)^{k}

n = 2 \sum \infty (\frac{3}{7})^{2 n}

n = 1 \sum \infty \frac{1}{1 - 4 n ^{2}}

n = 1 \sum \infty \frac{n ^{4}}{9 ^{n}}

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