sum from k=0 to infinity of (1/10)^k

Lösung

k = 0 \sum \infty (\frac{1}{10})^{k}

\frac{10}{9}

Dezimale

1.11111 \dots

Schritte zur Lösung

k = 0 \sum \infty (\frac{1}{10})^{k}

Geometrischen Test der Reihe anwenden:

\frac{10}{9}

= \frac{10}{9}

k = 1 \sum \infty 3 (- \frac{1}{5})^{3 k}

n = 0 \sum \infty - \frac{3}{( n ^{2} - 4 )}

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

n = 0 \sum \infty \frac{1}{n ^{\frac{5}{2}}}

n = 0 \sum \infty \frac{n}{e ^{7 n}}