sum from n=0 to infinity of [7(0.1)^n]

Lösung

n = 0 \sum \infty [7 (0.1)^{n}]

7.77777 \dots

Schritte zur Lösung

n = 0 \sum \infty 7 \cdot 0. 1^{n}

Wende die Regel der konstanten Multiplikation:

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

= 7 \cdot n = 0 \sum \infty 0. 1^{n}

Geometrischen Test der Reihe anwenden:

1.11111 \dots

= 7 \cdot 1.11111 \dots

Vereinfache

= 7.77777 \dots

n = 0 \sum \infty \frac{1}{5 + n}

k = 3 \sum \infty \frac{1}{4 k ^{2} - 1}

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

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

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