What is the sum from n=1 to infinity of (cos(8))^n ?

The sum from n=1 to infinity of (cos(8))^n is converges

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sum from n=1 to infinity of (cos(8))^n

n = 1 \sum \infty (cos (8))^{n}

converges

Solution steps

n = 1 \sum \infty (cos (8))^{n}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= n = 0 \sum \infty (cos (8))^{n} - (cos (8))^{0}

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

converges

= converges - (cos (8))^{0}

= converges

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

n = 1 \sum \infty \frac{5}{n ^{2} + 4}

n = 0 \sum \infty \frac{n}{3 n ^{2} + 1}

j = 1 \sum \infty 3^{- 3 j}

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

What is the sum from n=1 to infinity of (cos(8))^n ?
The sum from n=1 to infinity of (cos(8))^n is converges