erweitern (n(n+1)(2n+7))/6

Lösung

erweitern

\frac{n ( n + 1 ) ( 2 n + 7 )}{6}

\frac{n ^{3}}{3} + \frac{3 n ^{2}}{2} + \frac{7 n}{6}

Schritte zur Lösung

\frac{n ( n + 1 ) ( 2 n + 7 )}{6}

Multipliziere aus

n (n + 1) (2 n + 7) : 2 n^{3} + 9 n^{2} + 7 n

= \frac{2 n ^{3} + 9 n ^{2} + 7 n}{6}

Wende Bruchregel an:

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

\frac{2 n ^{3} + 9 n ^{2} + 7 n}{6} = \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{7 n}{6}

= \frac{2 n ^{3}}{6} + \frac{9 n ^{2}}{6} + \frac{7 n}{6}

Streiche

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

= \frac{n ^{3}}{3} + \frac{9 n ^{2}}{6} + \frac{7 n}{6}

Streiche

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

= \frac{n ^{3}}{3} + \frac{3 n ^{2}}{2} + \frac{7 n}{6}

e x p an d (sin^{(4)} (θ) - cos^{(4)} (θ) + 1) csc^{2} (x)

e x p an d \frac{5 x ^{2} - 80 x - 480}{( x - 8 ) ^{2}}

e x p an d 9 (n (n + 1) (2 n + 1))

e x p an d sin (\frac{( 2 n + 1 ) π}{2})

e x p an d 3 (- sec (x) + 2 sec^{3} (x)) + 3 sec (x) tan (x)