//---------------------
for b == 1 result: 1.000000000000000
for b == 2 result: 0.500000000000000
for b == 3 result: 0.333333333333333
for b == 4 result: 0.250000000000000
for b == 5 result: 0.200000000000000
for b == 6 result: 0.166666666666667
for b == 7 result: 0.142857142857143
for b == 8 result: 0.125000000000000
for b == 9 result: 0.111111111111111
for b == 10 result: 0.100000000000000
for b == 11 result: 0.090909090909091
for b == 12 result: 0.083333333333333
for b == 13 result: 0.076923076923077
for b == 14 result: 0.071428571428571
for b == 15 result: 0.066666666666667
for b == 16 result: 0.062500000000000
for b == 17 result: 0.058823529411765
for b == 18 result: 0.055555555555556
for b == 19 result: 0.052631578947368
for b == 20 result: 0.050000000000000
for b == 21 result: 0.047619047619048
for b == 22 result: 0.045454545454545
for b == 23 result: 0.043478260869565
for b == 24 result: 0.041666666666667
for b == 25 result: 0.040000000000000
for b == 26 result: 0.038461538461538
for b == 27 result: 0.037037037037037
for b == 28 result: 0.035714285714286
for b == 29 result: 0.034482758620690