sum from k=0 to infinity of 2/(k^2+k)

Lösung

k = 0 \sum \infty \frac{2}{k ^{2} + k}

2

Schritte zur Lösung

k = 1 \sum \infty \frac{2}{k ^{2} + k}

Wende die Regel der konstanten Multiplikation:

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

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

Teleskopreihen-Test anwenden:

1

= 2 \cdot 1

Vereinfache

= 2

n = 1 \sum \infty \frac{1}{5 ^{3 n}}

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

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

n = 1 \sum \infty \frac{1}{ln ( 5 ^{n} )}

n = 0 \sum \infty (\frac{1}{1.02})^{n}