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

The sum from n=1 to infinity of (sin(8))^n is 1/(1-sin(8))-1

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

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

\frac{1}{1 - sin ( 8 )} - 1

Decimal

92.96947 \dots

Solution steps

n = 1 \sum \infty (sin (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 (sin (8))^{n} - (sin (8))^{0}

n = 0 \sum \infty (sin (8))^{n} = \frac{1}{1 - sin ( 8 )}

= \frac{1}{1 - sin ( 8 )} - (sin (8))^{0}

Simplify

= \frac{1}{1 - sin ( 8 )} - 1

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What is the sum from n=1 to infinity of (sin(8))^n ?
The sum from n=1 to infinity of (sin(8))^n is 1/(1-sin(8))-1