What is the sum from n=1 to infinity of cos^n(0.6) ?

The sum from n=1 to infinity of cos^n(0.6) is 4.72526…

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sum from n=1 to infinity of cos^n(0.6)

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

4.72526 \dots

Solution steps

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

Simplify

cos (0.6) : 0.82533 \dots

= n = 1 \sum \infty 0.82533 \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 0.82533 \dots^{n} - 0.82533 \dots^{0}

n = 0 \sum \infty 0.82533 \dots^{n} = 5.72526 \dots

= 5.72526 \dots - 0.82533 \dots^{0}

Simplify

= 4.72526 \dots

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What is the sum from n=1 to infinity of cos^n(0.6) ?
The sum from n=1 to infinity of cos^n(0.6) is 4.72526…