sum from n=2 to infinity of |(ln(n))/n |

解答

n = 2 \sum \infty \frac{ln ( n )}{n}

发散

求解步骤

n = 2 \sum \infty \frac{ln ( n )}{n}

化简

\frac{ln ( n )}{n} : \frac{∣ ln ( n ) ∣}{∣ n ∣}

= n = 2 \sum \infty \frac{∣ ln ( n ) ∣}{∣ n ∣}

使用级数积分审敛法:

发散

= 发散

x = 0 \sum \infty \frac{x}{1 - 4 x}

n = 3 \sum \infty \frac{1}{n \cdot ln ( n )}

n = 1 \sum \infty \frac{n}{n ^{n}}

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

n = 1 \sum \infty \frac{7}{5 n - 1}