Hint to puzzle 34: Harmonic sum 2
Consider the table below, which shows Hn, for n = 2 to 10. The denominator is equal to the least common multiple of 2, 3, ..., n; and is therefore always even. Notice that, in each case, the numerator is odd. Is this true for all n > 1?
| n | Hn |
|---|---|
| 2 | 3/2 |
| 3 | 11/6 |
| 4 | 25/12 |
| 5 | 137/60 |
| 6 | 147/60 |
| 7 | 1089/420 |
| 8 | 2283/840 |
| 9 | 7129/2520 |
| 10 | 7381/2520 |