sum from n=0 to infinity of 3(3/4)^n

Lösung

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

12

Schritte zur Lösung

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

Wende die Regel der konstanten Multiplikation:

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

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

Geometrischen Test der Reihe anwenden:

4

= 3 \cdot 4

Vereinfache

= 12

n = 1 \sum \infty \frac{2 n + 1}{n + 2}

n = 0 \sum \infty \frac{- 3}{n ^{2} - 4}

n = 0 \sum \infty \frac{1}{n ^{100}}

n = 0 \sum \infty \frac{n ^{4}}{2 ^{n}}

m = 2 \sum \infty \frac{2}{5 ^{m}}