sum from n=0 to infinity of-6*(6/7)^n

解答

n = 0 \sum \infty - 6 \cdot (\frac{6}{7})^{n}

- 42

求解步骤

n = 0 \sum \infty - 6 (\frac{6}{7})^{n}

使用常数相乘法则:

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

= - 6 \cdot n = 0 \sum \infty (\frac{6}{7})^{n}

使用几何级数审敛法:

7

= - 6 \cdot 7

化简

= - 42

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