sum from n=1 to infinity}(-1)^{n+1 of (3/(2^n))

解答

n = 1 \sum \infty (- 1)^{n + 1} (\frac{3}{2 ^{n}})

收敛

求解步骤

n = 1 \sum \infty (- 1)^{n + 1} \frac{3}{2 ^{n}}

使用常数相乘法则:

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

= 3 \cdot n = 1 \sum \infty (- 1)^{n + 1} \frac{1}{2 ^{n}}

使用交错级数审敛法:

收敛

= 3 收敛

= 收敛

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