sum from k=0 to infinity of (0.25)^k

Lösung

k = 0 \sum \infty (0.25)^{k}

1.33333 \dots

Schritte zur Lösung

k = 0 \sum \infty 0.2 5^{k}

Geometrischen Test der Reihe anwenden:

1.33333 \dots

= 1.33333 \dots

n = 0 \sum \infty (n - 1)^{2}

n = 0 \sum \infty \frac{1}{2 n ^{2}}

n = 1 \sum \infty \frac{6 ^{n}}{n ^{k}}

n = 5 \sum \infty \frac{3}{2 ^{n}}

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