展开 (((n+k)(n+k)!))/(k!n!)

解答

展开

\frac{( ( n + k ) ( n + k ) ! )}{k ! n !}

\frac{n ( n + k ) !}{k ! n !} + \frac{k ( n + k ) !}{k ! n !}

求解步骤

\frac{( n + k ) ( n + k ) !}{k ! n !}

乘开

(n + k) (n + k)! : n (n + k)! + k (n + k)!

= \frac{n ( n + k ) ! + k ( n + k ) !}{k ! n !}

使用分式法则:

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

\frac{n ( n + k ) ! + k ( n + k ) !}{k ! n !} = \frac{n ( n + k ) !}{k ! n !} + \frac{k ( n + k ) !}{k ! n !}

= \frac{n ( n + k ) !}{k ! n !} + \frac{k ( n + k ) !}{k ! n !}

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