What is the sum from k=1 to infinity of (cos(10))^k ?

The sum from k=1 to infinity of (cos(10))^k is converges

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sum from k=1 to infinity of (cos(10))^k

k = 1 \sum \infty (cos (10))^{k}

converges

Solution steps

k = 1 \sum \infty (cos (10))^{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 (10))^{k} - (cos (10))^{0}

k = 0 \sum \infty (cos (10))^{k} =

converges

= converges - (cos (10))^{0}

= converges

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{3}

n = 1 \sum \infty cos (\frac{16}{n})

n = 1 \sum \infty \frac{1}{n ^{4} + 2 n + 8}

n = 0 \sum \infty \frac{n}{n + 4}

n = 0 \sum \infty \frac{3}{n ( n + 2 )}

What is the sum from k=1 to infinity of (cos(10))^k ?
The sum from k=1 to infinity of (cos(10))^k is converges