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Beliebt Rechnen >

sum from n=1 to infinity of 5/(7^n)

Lösung

n = 1 \sum \infty \frac{5}{7 ^{n}}

Lösung

\frac{5}{6}

+1

Dezimale

0.83333 \dots

Schritte zur Lösung

n = 1 \sum \infty \frac{5}{7 ^{n}}

Wende die Regel der konstanten Multiplikation:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{7 ^{n}}

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

= 5 (n = 0 \sum \infty \frac{1}{7 ^{n}} - \frac{1}{7 ^{0}})

n = 0 \sum \infty \frac{1}{7 ^{n}} = \frac{7}{6}

= 5 (\frac{7}{6} - \frac{1}{7 ^{0}})

Vereinfache

5 (\frac{7}{6} - \frac{1}{7 ^{0}}) : \frac{5}{6}

= \frac{5}{6}

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