展开 (n+1)(n/2)(n)

解答

展开

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

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

求解步骤

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

化简

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

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

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

使用分配律:

a (b + c) = ab + a c

n \frac{n}{2} (n + 1) = n \frac{n}{2} n + n \frac{n}{2} \cdot 1

= n \frac{n}{2} n + n \frac{n}{2} \cdot 1

化简

n \frac{n}{2} n + n \frac{n}{2} \cdot 1 : \frac{n ^{3} + n ^{2}}{2}

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

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