簡約 (n(n+1)}{2*(n\frac{(n+1))/2)^2}

解

簡約

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

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

解答ステップ

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

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

n^{2} = nn

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

共通因数を約分する:

n

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

簡素化

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

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