sum from n=1 to infinity of (n!)/(2n)

解答

n = 1 \sum \infty \frac{n !}{2 n}

发散

求解步骤

n = 1 \sum \infty \frac{n !}{2 n}

使用常数相乘法则:

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

= \frac{1}{2} \cdot n = 1 \sum \infty \frac{n !}{n}

使用级数比值审敛法:

发散

= \frac{1}{2} 发散

= 发散

n = 1 \sum \infty n^{- 0.6}

n = 0 \sum \infty \frac{4}{9 - n ^{2}}

k = 1 \sum \infty \frac{3}{k} - \frac{3}{k + 2}

n = 1 \sum \infty \frac{6 n}{6 n + 1}

n = 1 \sum \infty \frac{1}{n} - \frac{2}{3 n - 1}