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Beliebt Rechnen >

sum from n=1 to infinity of (8^n)/(9^n)

Lösung

n = 1 \sum \infty \frac{8 ^{n}}{9 ^{n}}

Lösung

8

Schritte zur Lösung

n = 1 \sum \infty \frac{8 ^{n}}{9 ^{n}}

Wende Exponentenregel an:

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

= n = 1 \sum \infty (\frac{8}{9})^{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{8}{9})^{n} - (\frac{8}{9})^{0}

n = 0 \sum \infty (\frac{8}{9})^{n} = 9

= 9 - (\frac{8}{9})^{0}

Vereinfache

= 8

Beliebte Beispiele

integral from-infinity to-1 of 1/(x^3)

\int_{- \infty}^{- 1} \frac{1}{x ^{3}} d x

derivative of 1-2sin(x)

\frac{d}{d x} (1 - 2 sin (x))

derivative f(x)=6e^x

d er i v a t i v e f (x) = 6 e^{x}

limit as h approaches+6 of (4h)/(h-6)

h \to + 6 lim (\frac{4 h}{h - 6})

f (x) = 9 - x