展开 ((n(n+1)(n+2)))/6

解答

展开

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

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

求解步骤

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

乘开

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

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

使用分式法则:

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

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

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

消掉

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

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

消掉

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

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

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

e x p an d \frac{2 x ^{2} + 5 x + 7}{( x + 1 ) ( x ^{2} + x + 1 )}

e x p an d \frac{s ^{2} + 2 - e ^{- s}}{s ( s ^{2} + 16 )}

e x p an d A (2, - 3) e B (- 2, 1)

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