What is the sum from n=1 to infinity of cos^n(0.8) ?

The sum from n=1 to infinity of cos^n(0.8) is 2.29713…

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sum from n=1 to infinity of cos^n(0.8)

n = 1 \sum \infty cos^{n} (0.8)

2.29713 \dots

Solution steps

n = 1 \sum \infty cos^{n} (0.8)

Simplify

cos (0.8) : 0.69670 \dots

= n = 1 \sum \infty 0.69670 \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 0.69670 \dots^{n} - 0.69670 \dots^{0}

n = 0 \sum \infty 0.69670 \dots^{n} = 3.29713 \dots

= 3.29713 \dots - 0.69670 \dots^{0}

Simplify

= 2.29713 \dots

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What is the sum from n=1 to infinity of cos^n(0.8) ?
The sum from n=1 to infinity of cos^n(0.8) is 2.29713…