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I am working on a problem that states:

Find a closed form expression for the following double summation in terms of n:

$\sum_{j=1}^n\sum_{k=j}^n\frac{1}{k}$

My professor said I should be solving this with a table, but I cannot find any examples of this aside from this table in the notes:

https://i.stack.imgur.com/r8PnI.png

So my question is how should I go about creating a table that helps me find the closed form of the double summation?

Matthetart
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  • Approach is analogous, your table is only upper triangular in this case – PinkyWay Oct 16 '23 at 20:16
  • $$\begin{matrix}1&\frac12&\frac13&\ldots&\frac1n\0&\frac12&\frac13&\ldots&\frac1n\0&0&\frac13&\ldots&\frac1n\0&0&0&\ldots&\frac1n\\vdots&\vdots&\vdots&\ddots&\vdots\0&0&0&\ldots&\frac1n\end{matrix}$$ – PinkyWay Oct 16 '23 at 20:25

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