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Beliebt Rechnen >

sum from n=1 to infinity of 1/(n(n+2))

Lösung

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

Lösung

\frac{3}{4}

+1

Dezimale

0.75

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{n ( n + 2 )} : \frac{1}{2 n} - \frac{1}{2 ( n + 2 )}

= n = 1 \sum \infty \frac{1}{2 n} - \frac{1}{2 ( n + 2 )}

Erweitere die Teleskopreihe:

\frac{3}{4}

= \frac{3}{4}

Beliebte Beispiele

tangent sqrt(1-4x)

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sum from n=1 to infinity of ((1))/(n^2)

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

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limit as x approaches 0+of arcsin(2x-1)

x \to 0 + lim (arcsin (2 x - 1))