erweitern ([n(n+1)(2(n)+1)])/6-n

Lösung

erweitern

\frac{[ n ( n + 1 ) ( 2 ( n ) + 1 ) ]}{6} - n

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

Schritte zur Lösung

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

Entferne die Klammern:

(a) = a

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

Multipliziere aus

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

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

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} - n

Streiche

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

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

Streiche

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

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

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