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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Wende Regel an

\frac{a}{a} = 1

\frac{6}{6} = 1

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

Streiche

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

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

Streiche

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

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

e x p an d \frac{( x ^{4} + x ^{2} + 1 ) ( x ^{8} + x ^{4} + x ^{2} + 1 )}{x ^{4} + 2 x + 4}

e x p an d (4 + e)^{2}

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

e x p an d \frac{( 1 - x ^{3} + x ^{2} ) ( 1 - x ^{2} + x ^{3} )}{1 - x ^{3} - x ^{2}}

e x p an d \frac{5}{( s ^{2} + 1 ) ( s ^{2} + 2 s + 2 )}