展開する (sum_{(k=1)}(1+k))/(((2+k)!))

解

展開する

\frac{s u m _{(k = 1)} ( 1 + k )}{( ( 2 + k ) ! )}

\frac{m _{(k = 1)} s u}{( 2 + k ) !} + \frac{m _{(k = 1)} k s u}{( 2 + k ) !}

解答ステップ

\frac{s u m _{(k = 1)} ( 1 + k )}{( 2 + k ) !}

拡張

s u m_{(k = 1)} (1 + k) : m_{(k = 1)} s u + m_{(k = 1)} k s u

= \frac{m _{(k = 1)} s u + m _{(k = 1)} k s u}{( 2 + k ) !}

分数の規則を適用する:

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

\frac{m _{(k = 1)} s u + m _{(k = 1)} k s u}{( 2 + k ) !} = \frac{m _{(k = 1)} s u}{( 2 + k ) !} + \frac{m _{(k = 1)} k s u}{( 2 + k ) !}

= \frac{m _{(k = 1)} s u}{( k + 2 ) !} + \frac{m _{(k = 1)} k s u}{( k + 2 ) !}