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 (\frac{6}{7} - x)^{4}

e x p an d (y^{2} - 2 x y + 6 x) d x + (x^{2} - 2 x y + 2) d y

s im pl i f y (a + 2 + \frac{7}{a - 5}) (a - 2 - \frac{5}{a + 2})

e x p an d (a + b)^{3}

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