erweitern ((n(n+1)(2n+1)))/6

Lösung

erweitern

\frac{( n ( n + 1 ) ( 2 n + 1 ) )}{6}

\frac{n ^{3}}{3} + \frac{n ^{2}}{2} + \frac{n}{6}

Schritte zur Lösung

\frac{n ( n + 1 ) ( 2 n + 1 )}{6}

Multipliziere aus

n (n + 1) (2 n + 1) : 2 n^{3} + 3 n^{2} + n

= \frac{2 n ^{3} + 3 n ^{2} + n}{6}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 n ^{3} + 3 n ^{2} + n}{6} = \frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6}

= \frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6}

Streiche

\frac{2 n ^{3}}{6} : \frac{n ^{3}}{3}

= \frac{n ^{3}}{3} + \frac{3 n ^{2}}{6} + \frac{n}{6}

Streiche

\frac{3 n ^{2}}{6} : \frac{n ^{2}}{2}

= \frac{n ^{3}}{3} + \frac{n ^{2}}{2} + \frac{n}{6}

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