sum from n=1 to infinity of (80)/(8^n)

解答

n = 1 \sum \infty \frac{80}{8 ^{n}}

\frac{80}{7}

十进制

11.42857 \dots

求解步骤

n = 1 \sum \infty \frac{80}{8 ^{n}}

使用常数相乘法则:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 80 \cdot n = 1 \sum \infty \frac{1}{8 ^{n}}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= 80 (n = 0 \sum \infty \frac{1}{8 ^{n}} - \frac{1}{8 ^{0}})

n = 0 \sum \infty \frac{1}{8 ^{n}} = \frac{8}{7}

= 80 (\frac{8}{7} - \frac{1}{8 ^{0}})

化简

80 (\frac{8}{7} - \frac{1}{8 ^{0}}) : \frac{80}{7}

= \frac{80}{7}

\int 4 e^{x + y}

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d er i v a t i v e f (x) = \frac{1}{t ^{2}}

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