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受欢迎的微积分 >

sum from n=0 to infinity of 2*0.2^n

解答

n = 0 \sum \infty 2 \cdot 0. 2^{n}

解答

2.5

求解步骤

n = 0 \sum \infty 2 \cdot 0. 2^{n}

使用常数相乘法则:

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

= 2 \cdot n = 0 \sum \infty 0. 2^{n}

使用几何级数审敛法:

1.25

= 2 \cdot 1.25

化简

= 2.5

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