sum from n=0 to infinity of 5(3/pi)^n

Lösung

n = 0 \sum \infty 5 (\frac{3}{π})^{n}

5 \cdot \frac{π}{π - 3}

Dezimale

110.93769 \dots

Schritte zur Lösung

n = 0 \sum \infty 5 (\frac{3}{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{3}{π})^{n}

Geometrischen Test der Reihe anwenden:

\frac{π}{π - 3}

= 5 \cdot \frac{π}{π - 3}

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

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

n = 2 \sum \infty \frac{1}{ln ( n ^{3} )}

n = 3 \sum \infty 5 (\frac{4}{9})^{n}

n = 1 \sum \infty \frac{5}{n ^{2} + 121}