sum from n=0 to infinity of 1/6 (5/6)^n

Lösung

n = 0 \sum \infty \frac{1}{6} (\frac{5}{6})^{n}

1

Schritte zur Lösung

n = 0 \sum \infty \frac{1}{6} (\frac{5}{6})^{n}

Wende die Regel der konstanten Multiplikation:

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

= \frac{1}{6} \cdot n = 0 \sum \infty (\frac{5}{6})^{n}

Geometrischen Test der Reihe anwenden:

6

= \frac{1}{6} \cdot 6

Vereinfache

\frac{1}{6} \cdot 6 : 1

= 1

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

n = 1 \sum \infty \frac{10 0 ^{n}}{n !}

n = 1 \sum \infty n ln (n)

k = 2 \sum \infty \frac{1}{k ^{2} - 1}

n = 1 \sum \infty n^{- 0.8}