sum from n=0 to infinity of 4*(-1/8)^n

解答

n = 0 \sum \infty 4 \cdot (- \frac{1}{8})^{n}

\frac{32}{9}

十进制

3.55555 \dots

求解步骤

n = 0 \sum \infty 4 (- \frac{1}{8})^{n}

使用常数相乘法则:

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

= 4 \cdot n = 0 \sum \infty (- \frac{1}{8})^{n}

使用几何级数审敛法:

\frac{8}{9}

= 4 \cdot \frac{8}{9}

化简

4 \cdot \frac{8}{9} : \frac{32}{9}

= \frac{32}{9}

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