Summing over n variables

Question

I am currently trying to create a function taht will sum over n variables, but I don't really know how ot implement it. It should look like this:

$$f[n]=\left(\frac{1}{6}\right)^n \sum _{x_1=1}^6\sum _{x_2=1}^6...\sum _{x_n=1}^6 x_1+x_2+...+x_n - \min(x_1,...,x_n)$$

Sadly I have no idea how I can tell mathematica to create the exact right amounts of variables and sums. Does anyone have an idea?

score 2 · Answer 1 · answered Oct 26 '14 at 19:58

2

f[n_] := 1/6^n Module[{xx = Array[x, n]},
                      Sum[Tr@xx - Min @@ xx, Evaluate[Sequence @@ ({#, 6} & /@ xx)]]]

answered Oct 26 '14 at 19:58

Dr. belisarius

Thank you. Your solution works perfectly and I understand what is going on. – Escapado Oct 26 '14 at 20:28

score 2 · Accepted Answer · answered Oct 26 '14 at 19:59

2

f[n_] := Total[Total[#] - Min[#] & /@ Tuples[Range[6], n]]/6^n;

answered Oct 26 '14 at 19:59

Per Alexandersson

Thank you for your reply aswell. Your solution also works! – Escapado Oct 26 '14 at 20:29

2 Answers2