Find an antidifference for the sequence $\left(H_{k} ight) $ defined by $$ H_{k}=\sum_{j=1}^{k} \frac{1}{j} $$ For inspiration, you can think about the integration by parts calculation that an antiderivative of $\log (x)$ is $$ x \log (x-x $$ and use the discrete analogue of integration by parts: $$ \sum_{k=a}^{b} u_{k} \Delta v_{k}=\left[u_{k} v_{k} ight]{a}^{b+1} - \sum_{k=a}^{b} v_{k+1} \Delta u_{k}, $$ where $\Delta$ denotes the forward difference operator $\Delta S_{k}=s_{k+1}-s_{k}$. CS.VS. 1717||