How do I find the sum with given $\alpha$: $$\sum_{k=1}^{n}\frac{\alpha^{\underline{k}}}{k}=?$$ There's a tip in the task to find $\Delta \alpha^{\underline{n}}=\alpha^{\underline{n+1}}-\alpha^{\underline{n}}$. So we get $$\Delta \alpha^{\underline{n}}=\alpha^{\underline{n}}(\alpha-n-1)$$ I can't see any connection between sum and this equation.
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1What is the significance of the underline under the index $k$ in: $\alpha^{\underline{k}}$? – uniquesolution Nov 05 '15 at 10:08