A arte de calcular VII

1 x 7 + 3 = 10
14 x 7 + 2 = 100
142 x 7 + 6 = 1000
1428 x 7 + 4 = 10000
14285 x 7 + 5 = 100000
142857 x 7 + 1 = 1000000
1428571 x 7 + 3 = 10000000
14285714 x 7 + 2 = 100000000
142857142 x 7 + 6 = 1000000000
1428571428 x 7 + 4 = 10000000000
14285714285 x 7 + 5 = 100000000000
142857142857 x 7 + 1 = 1000000000000