展开 [(k(k+1))/2 ]+(k+1)

解答

展开

[\frac{k ( k + 1 )}{2}] + (k + 1)

\frac{k ^{2}}{2} + \frac{k}{2} + k + 1

求解步骤

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

去除括号:

(a) = a

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

乘开

k (k + 1) : k^{2} + k

= \frac{k ^{2} + k}{2} + k + 1

使用分式法则:

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

\frac{k ^{2} + k}{2} = \frac{k ^{2}}{2} + \frac{k}{2}

= \frac{k ^{2}}{2} + \frac{k}{2} + k + 1

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