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}

e x p an d u (u^{2} + 3 u + 7)

s im pl i f y (- 2 n p + n) (n - n)

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

e x p an d \frac{12 x}{( x ^{2} + 3 ) ^{2}}

e x p an d \frac{( x - 4 y ) ^{2}}{x ^{5} + 64 x ^{2} y ^{3}}