展开 (n(n+1)(n+2)(n+3))/4

解答

展开

\frac{n ( n + 1 ) ( n + 2 ) ( n + 3 )}{4}

\frac{n ^{4}}{4} + \frac{3 n ^{3}}{2} + \frac{11 n ^{2}}{4} + \frac{3 n}{2}

求解步骤

\frac{n ( n + 1 ) ( n + 2 ) ( n + 3 )}{4}

乘开

n (n + 1) (n + 2) (n + 3) : n^{4} + 6 n^{3} + 11 n^{2} + 6 n

= \frac{n ^{4} + 6 n ^{3} + 11 n ^{2} + 6 n}{4}

使用分式法则:

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

\frac{n ^{4} + 6 n ^{3} + 11 n ^{2} + 6 n}{4} = \frac{n ^{4}}{4} + \frac{6 n ^{3}}{4} + \frac{11 n ^{2}}{4} + \frac{6 n}{4}

= \frac{n ^{4}}{4} + \frac{6 n ^{3}}{4} + \frac{11 n ^{2}}{4} + \frac{6 n}{4}

消掉

\frac{6 n ^{3}}{4} : \frac{3 n ^{3}}{2}

= \frac{n ^{4}}{4} + \frac{3 n ^{3}}{2} + \frac{11 n ^{2}}{4} + \frac{6 n}{4}

消掉

\frac{6 n}{4} : \frac{3 n}{2}

= \frac{n ^{4}}{4} + \frac{3 n ^{3}}{2} + \frac{11 n ^{2}}{4} + \frac{3 n}{2}

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e x p an d \frac{d}{d x} ((100 - 2 x) \cdot x) - x^{2}

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

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

e x p an d (2 x y + y^{2}) ∣ (1, 0) ∣