Summation of Odd Reciprocals in terms of Harmonic Numbers/Historical Note

Historical Note on Summation of Odd Reciprocals in terms of Harmonic Numbers
originally published the following result in ($1997$) as a solution to the exercise to evaluate $\displaystyle \sum_{k \mathop = 1}^n \dfrac 1 {2 k - 1}$:
 * $\displaystyle \sum_{k \mathop = 1}^n \dfrac 1 {2 k - 1} = H_{2 n - 1} - \dfrac {H_{n - 1} } 2$

The online errata sheet, found via https://www-cs-faculty.stanford.edu/~knuth/taocp.html, offers the simpler result as a replacement.