I want something like

f[n] = Sum[2^Sum[i_k, {k, n}], {i_1, Infinity}, {i_2, Infinity},...{i_n, Infinity}]

I'm playing with:

Table[i_k, {k, n}]

But can't find a way to parse it in the definition.

What's the good way to do it?


1 Answer 1


Try this:

With[{n = 5}, 
     Inactive[Sum][a^Sum[K[i], {i, n}], ##] & @@ 
     Table[{K[i], 1, ∞}, {i, n}]]

$$\sum_{\mathtt{K[1]}=1}^\infty \sum_{\mathtt{K[2]}=1}^\infty \sum_{\mathtt{K[3]}=1}^\infty \sum_{\mathtt{K[4]}=1}^\infty \sum_{\mathtt{K[5]}=1}^\infty a^{\mathtt{K[1]}+\mathtt{K[2]}+\mathtt{K[3]}+\mathtt{K[4]}+\mathtt{K[5]}}$$

Replace Inactive[Sum] with Sum to see the actual result of the evaluation.

  • $\begingroup$ OK. ## is the key I want. Thanks. $\endgroup$
    – tcya
    Commented Apr 20, 2017 at 5:22

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