sum from k=2 to infinity of 8/(4^{2k)}

Lösung

k = 2 \sum \infty \frac{8}{4 ^{2 k}}

\frac{1}{30}

Dezimale

0.03333 \dots

Schritte zur Lösung

k = 2 \sum \infty \frac{8}{4 ^{2 k}}

Wende die Regel der konstanten Multiplikation:

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

= 8 \cdot k = 2 \sum \infty \frac{1}{4 ^{2 k}}

4^{2 k} = 1 6^{k}

= 8 \cdot k = 2 \sum \infty \frac{1}{1 6 ^{k}}

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

= 8 (k = 0 \sum \infty \frac{1}{1 6 ^{k}} - \frac{1}{1 6 ^{0}} - \frac{1}{1 6 ^{1}})

k = 0 \sum \infty \frac{1}{1 6 ^{k}} = \frac{16}{15}

= 8 (\frac{16}{15} - \frac{1}{1 6 ^{0}} - \frac{1}{1 6 ^{1}})

Vereinfache

8 (\frac{16}{15} - \frac{1}{1 6 ^{0}} - \frac{1}{1 6 ^{1}}) : \frac{1}{30}

= \frac{1}{30}

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

\int 6 x 1 - 3 x^{2} d x

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

\frac{\partial}{\partial x} (3 y^{2} e^{x} - 4 x)

\frac{\partial}{\partial x} (x^{2} yz)