Home / b_4 = \frac{46}{81} - \frac{1}{3} \cdot \frac{97336}{531441} = \frac{46}{81} - \frac{97336}{1594323}

b_4 = \frac{46}{81} - \frac{1}{3} \cdot \frac{97336}{531441} = \frac{46}{81} - \frac{97336}{1594323}

February 22, 2026

$b_4 = \frac{46}{81} - \frac{1}{3} \cdot \frac{97336}{531441} = \frac{46}{81} - \frac{97336}{1594323}$

$ b_3 = M(b_2) = \frac{2}{3} - \frac{(\frac{2}{3})^3}{3} = \frac{2}{3} - \frac{8}{81} = \frac{54 - 8}{81} = \frac{46}{81} $
$ b_4 = M(b_3) = \frac{46}{81} - \frac{(\frac{46}{81})^3}{3} $
First, compute $ \left( \frac{46}{81} \right)^3 = \frac{97336}{531441} $, so
Convert $ \frac{46}{81} $ to denominator $ 1594323 $:
\frac{46}{81} = \frac{46 \cdot 19683}{1594323} = \frac{904518}{1594323}
b_4 = \frac{904518 - 97336}{1594323} = \frac{807182}{1594323}