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Beliebt Rechnen >

sum from n=1 to infinity of (9^n)/(10^n)

Lösung

n = 1 \sum \infty \frac{9 ^{n}}{1 0 ^{n}}

Lösung

9

Schritte zur Lösung

n = 1 \sum \infty \frac{9 ^{n}}{1 0 ^{n}}

Wende Exponentenregel an:

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

= n = 1 \sum \infty (\frac{9}{10})^{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{9}{10})^{n} - (\frac{9}{10})^{0}

n = 0 \sum \infty (\frac{9}{10})^{n} = 10

= 10 - (\frac{9}{10})^{0}

Vereinfache

= 9

Beliebte Beispiele

integral of sec^3(8x)

\int sec^{3} (8 x) d x

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\int x^{2} 2 x + 5 d x

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y^{''}+4y^'+4y=t+e^{2t}

y^{^{''}} + 4 y^{^{'}} + 4 y = t + e^{2 t}