erweitern (((n+1)(n+2)(2*n+3)))/6

Lösung

erweitern

\frac{( ( n + 1 ) \cdot ( n + 2 ) \cdot ( 2 \cdot n + 3 ) )}{6}

\frac{n ^{3}}{3} + \frac{3 n ^{2}}{2} + \frac{13 n}{6} + 1

Schritte zur Lösung

\frac{( n + 1 ) ( n + 2 ) ( 2 n + 3 )}{6}

Multipliziere aus

(n + 1) (n + 2) (2 n + 3) : 2 n^{3} + 9 n^{2} + 13 n + 6

= \frac{2 n ^{3} + 9 n ^{2} + 13 n + 6}{6}

Wende Bruchregel an:

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

\frac{2 n ^{3} + 9 n ^{2} + 13 n + 6}{6} = \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + \frac{6}{6}

= \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + \frac{6}{6}

Wende Regel an

\frac{a}{a} = 1

\frac{6}{6} = 1

= \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + 1

Streiche

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

= \frac{n ^{3}}{3} + \frac{9 n ^{2}}{6} + \frac{13 n}{6} + 1

Streiche

\frac{9 n ^{2}}{6} : \frac{3 n ^{2}}{2}

= \frac{n ^{3}}{3} + \frac{3 n ^{2}}{2} + \frac{13 n}{6} + 1

e x p an d \frac{x ^{2} - 6 x}{( x - 3 ) ^{2}}

e x p an d \frac{f ( x ) ( 8 x - 10 )}{( x - 1 )}

e x p an d (- y e^{- y} - e^{- y} + 1)^{2}

e x p an d tan (arctan (\frac{w}{o}) + 180 (2 k + 1))

e x p an d \frac{x ^{2} - 1}{x ^{2} + 2 x + 1}