sum from n=0 to infinity of 1/(3^{2n+1)}

解答

n = 0 \sum \infty \frac{1}{3 ^{2 n + 1}}

收敛

求解步骤

n = 0 \sum \infty \frac{1}{3 ^{2 n + 1}}

使用级数比值审敛法:

收敛

= 收敛

n = 0 \sum \infty \frac{6 ^{n}}{5 ^{n}}

n = 1 \sum \infty \frac{1}{2 n + 9}

n = 1 \sum \infty n^{9} (1 + n^{10})

n = 0 \sum \infty \frac{1}{n} - \frac{1}{n ^{2}}

n = 1 \sum \infty 4 arccos (\frac{1}{n})