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Beliebt Rechnen >

sum from n=1 to infinity of 7/(10^n)

Lösung

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

Lösung

\frac{7}{9}

+1

Dezimale

0.77777 \dots

Schritte zur Lösung

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

Wende die Regel der konstanten Multiplikation:

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

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

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

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

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

= 7 (\frac{10}{9} - \frac{1}{1 0 ^{0}})

Vereinfache

7 (\frac{10}{9} - \frac{1}{1 0 ^{0}}) : \frac{7}{9}

= \frac{7}{9}

Beliebte Beispiele

tangent f(x)=2x^3+36x^2+192x+8

t an g e n t f (x) = 2 x^{3} + 36 x^{2} + 192 x + 8

limit as x approaches 0+of (e^x)/(1-e^{-x)}

x \to 0 + lim (\frac{e ^{x}}{1 - e ^{- x}})

derivative of 4e^{6x}

\frac{d}{d x} (4 e^{6 x})

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d er i v a t i v e f (x) = sin (3 x + 1)

derivative of (4x^{6x})

\frac{d}{d x} ((4 x)^{6 x})