sum from n=0 to infinity of 5/(pi^n)

Lösung

n = 0 \sum \infty \frac{5}{π ^{n}}

5 \cdot \frac{π}{π - 1}

Dezimale

7.33471 \dots

Schritte zur Lösung

n = 0 \sum \infty \frac{5}{π ^{n}}

Wende die Regel der konstanten Multiplikation:

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

= 5 \cdot n = 0 \sum \infty \frac{1}{π ^{n}}

Geometrischen Test der Reihe anwenden:

\frac{π}{π - 1}

= 5 \cdot \frac{π}{π - 1}

\frac{d}{d x} (4 + 2 x - 3 x^{2} - 5 x^{3} - 8 x^{4} + 9 x^{5})

\int_{0}^{2 π} 20 + 16 t^{2} d t

x \to - 2 lim ((x + 1)^{4} (2 x^{2}))

d er i v a t i v e \frac{x ^{2} + 9}{x + 3}

\int_{0}^{2} \frac{1}{4 + x ^{2}} d x