簡約 1/(2sqrt(2))ln((sqrt(2)-1)/(sqrt(2)+1))

解

簡約

\frac{1}{2 2} ln (\frac{2 - 1}{2 + 1})

\frac{2}{4} (ln (2 - 1) - ln (2 + 1))

十進法表記

- 0.62322 \dots

解答ステップ

\frac{1}{2 2} ln (\frac{2 - 1}{2 + 1})

対数の規則を適用する:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{2 - 1}{2 + 1}) = ln (2 - 1) - ln (2 + 1)

= \frac{1}{2 2} (ln (2 - 1) - ln (1 + 2))

\frac{1}{2 2} = \frac{2}{4}

= \frac{2}{4} (ln (2 - 1) - ln (1 + 2))