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Beliebt Rechnen >

sum from n=1 to infinity of (10/17)^n

Lösung

n = 1 \sum \infty (\frac{10}{17})^{n}

Lösung

\frac{10}{7}

+1

Dezimale

1.42857 \dots

Schritte zur Lösung

n = 1 \sum \infty (\frac{10}{17})^{n}

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

= n = 0 \sum \infty (\frac{10}{17})^{n} - (\frac{10}{17})^{0}

n = 0 \sum \infty (\frac{10}{17})^{n} = \frac{17}{7}

= \frac{17}{7} - (\frac{10}{17})^{0}

Vereinfache

\frac{17}{7} - (\frac{10}{17})^{0} : \frac{10}{7}

= \frac{10}{7}

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