sum from n=6 to infinity of (3^n)/(12^n)

解答

n = 6 \sum \infty \frac{3 ^{n}}{1 2 ^{n}}

收敛

求解步骤

n = 6 \sum \infty \frac{3 ^{n}}{1 2 ^{n}}

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

L > 1,

由拉比判别法

= 收敛

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