sum from n=1 to infinity of 4(1/4)^n

Lösung

n = 1 \sum \infty 4 (\frac{1}{4})^{n}

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

n = 1 \sum \infty 4 (\frac{1}{4})^{n}

Wende die Regel der konstanten Multiplikation:

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

= 4 \cdot n = 1 \sum \infty (\frac{1}{4})^{n}

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

= 4 (n = 0 \sum \infty (\frac{1}{4})^{n} - (\frac{1}{4})^{0})

n = 0 \sum \infty (\frac{1}{4})^{n} = \frac{4}{3}

= 4 (\frac{4}{3} - (\frac{1}{4})^{0})

Vereinfache

4 (\frac{4}{3} - (\frac{1}{4})^{0}) : \frac{4}{3}

= \frac{4}{3}

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