sum from x=1 to infinity of (ln(x))/x

Lösung

x = 1 \sum \infty \frac{ln ( x )}{x}

divergiert

Schritte zur Lösung

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

Reihenintegraltest anwenden:

divergiert

= divergiert

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

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

n = 0 \sum \infty 3 + \frac{2}{n ^{4}}

n = 1 \sum \infty \frac{3}{n ^{9}}

n = 0 \sum \infty \frac{n ^{2}}{1 + 6 n}