(1/2) * 3 = 3/2 ⇒ 1 + 1/2
(1/2) * 3 = 3/2 ⇒ 1 + 1/2
(1/2) * 3 = 3/2 ⇒ 1 + 1/2
........
Read the numbers in red from bottom to top = .111...3
(1/7) base 8
(1/7) * 8 = 8/7 = 1 + 1/7
(1/7) * 8 = 8/7 = 1 + 1/7
(1/7) * 8 = 8/7 = 1 + 1/7
........
Read the red numbers from bottom to top = .111...8
So it appears that 1 / (b - 1) in base b is .111.....b
+429 