What is the sum from n=1 to infinity of (cos(0.3))^n ?

The sum from n=1 to infinity of (cos(0.3))^n is 21.38964…

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sum from n=1 to infinity of (cos(0.3))^n

n = 1 \sum \infty (cos (0.3))^{n}

21.38964 \dots

Solution steps

n = 1 \sum \infty (cos (0.3))^{n}

Simplify

cos (0.3) : 0.95533 \dots

= n = 1 \sum \infty 0.95533 \dots^{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 0.95533 \dots^{n} - 0.95533 \dots^{0}

n = 0 \sum \infty 0.95533 \dots^{n} = 22.38964 \dots

= 22.38964 \dots - 0.95533 \dots^{0}

Simplify

= 21.38964 \dots

\int \frac{csc ( x )}{csc ( x ) - sin ( x )} d x

\frac{d y}{d t} + y = t e^{t}

f (x) = \frac{1}{2 x}, at x = 36

f (x) = \frac{tan ( 9 x )}{1 + sin ( 9 x )}

What is the sum from n=1 to infinity of (cos(0.3))^n ?
The sum from n=1 to infinity of (cos(0.3))^n is 21.38964…