sum from n=0 to infinity of 9/(5^n)

Lösung

n = 0 \sum \infty \frac{9}{5 ^{n}}

\frac{45}{4}

Dezimale

11.25

Schritte zur Lösung

n = 0 \sum \infty \frac{9}{5 ^{n}}

Wende die Regel der konstanten Multiplikation:

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

= 9 \cdot n = 0 \sum \infty \frac{1}{5 ^{n}}

Geometrischen Test der Reihe anwenden:

\frac{5}{4}

= 9 \cdot \frac{5}{4}

Vereinfache

9 \cdot \frac{5}{4} : \frac{45}{4}

= \frac{45}{4}

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

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

k = 4 \sum \infty \frac{6}{k} - \frac{6}{k + 1}

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

k = n \sum \infty (\frac{3}{4})^{k} (\frac{1}{4})