sum from n=1 to infinity of (cos(1.4))^n

解答

n = 1 \sum \infty (cos (1.4))^{n}

0.20477 \dots

求解步骤

n = 1 \sum \infty (cos (1.4))^{n}

化简

cos (1.4) : 0.16996 \dots

= n = 1 \sum \infty 0.16996 \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 0.16996 \dots^{n} - 0.16996 \dots^{0}

n = 0 \sum \infty 0.16996 \dots^{n} = 1.20477 \dots

= 1.20477 \dots - 0.16996 \dots^{0}

化简

= 0.20477 \dots

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