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Beliebt Rechnen >

sum from n=0 to infinity of (2^n)/(5^n)

Lösung

n = 0 \sum \infty \frac{2 ^{n}}{5 ^{n}}

Lösung

\frac{5}{3}

+1

Dezimale

1.66666 \dots

Schritte zur Lösung

n = 0 \sum \infty \frac{2 ^{n}}{5 ^{n}}

Wende Exponentenregel an:

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

= n = 0 \sum \infty (\frac{2}{5})^{n}

Geometrischen Test der Reihe anwenden:

\frac{5}{3}

= \frac{5}{3}

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