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

解

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

21.38964 \dots

解答ステップ

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

簡素化

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}

簡素化

= 21.38964 \dots