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

解

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

4.72526 \dots

解答ステップ

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

簡素化

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}

簡素化

= 4.72526 \dots