What is the sum from n=1 to infinity of (cos(21))^n ?

The sum from n=1 to infinity of (cos(21))^n is converges

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sum from n=1 to infinity of (cos(21))^n

n = 1 \sum \infty (cos (21))^{n}

converges

Solution steps

n = 1 \sum \infty (cos (21))^{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 (21))^{n} - (cos (21))^{0}

n = 0 \sum \infty (cos (21))^{n} =

converges

= converges - (cos (21))^{0}

= converges

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

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

n = 0 \sum \infty arctan (\frac{1}{n})

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

n = 1 \sum \infty 3 (0.6)^{n - 1}

What is the sum from n=1 to infinity of (cos(21))^n ?
The sum from n=1 to infinity of (cos(21))^n is converges