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Beliebt Rechnen >

sum from n=1 to infinity of 15(1/100)^n

Lösung

n = 1 \sum \infty 15 (\frac{1}{100})^{n}

Lösung

\frac{5}{33}

+1

Dezimale

0.15151 \dots

Schritte zur Lösung

n = 1 \sum \infty 15 (\frac{1}{100})^{n}

Wende die Regel der konstanten Multiplikation:

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

= 15 \cdot n = 1 \sum \infty (\frac{1}{100})^{n}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= 15 (n = 0 \sum \infty (\frac{1}{100})^{n} - (\frac{1}{100})^{0})

n = 0 \sum \infty (\frac{1}{100})^{n} = \frac{100}{99}

= 15 (\frac{100}{99} - (\frac{1}{100})^{0})

Vereinfache

15 (\frac{100}{99} - (\frac{1}{100})^{0}) : \frac{5}{33}

= \frac{5}{33}

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