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Beliebt Rechnen >

sum from n=1 to infinity of (-3^n)/(8^n)

Lösung

n = 1 \sum \infty \frac{- 3 ^{n}}{8 ^{n}}

Lösung

- \frac{3}{5}

+1

Dezimale

- 0.6

Schritte zur Lösung

n = 1 \sum \infty \frac{- 3 ^{n}}{8 ^{n}}

Wende die Regel der konstanten Multiplikation:

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

= - n = 1 \sum \infty \frac{3 ^{n}}{8 ^{n}}

Wende Exponentenregel an:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

= - n = 1 \sum \infty (\frac{3}{8})^{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{3}{8})^{n} - (\frac{3}{8})^{0})

n = 0 \sum \infty (\frac{3}{8})^{n} = \frac{8}{5}

= - (\frac{8}{5} - (\frac{3}{8})^{0})

Vereinfache

- (\frac{8}{5} - (\frac{3}{8})^{0}) : - \frac{3}{5}

= - \frac{3}{5}

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