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Problem with the Sum Function -- Using a Benford Distribution


 
 (* define a PDF*)
 f = Log[10, 1 + 1/d]
 
 
 (* compute for various values of the parameter *)
 Table[Apply[Plus, Table[f, {d, 10 ^ h, 10 ^ (h + 1) - 1}]], {h, 0, 4}]// N
 
 
 (* the mean is well defined *)
 Table[ Apply[Plus, Table[d  Log[10, 1 + 1/d], {d, 10^h, 10^(h + 1) - 1}]] //N,
 {h, 0, 4}] 
 
 (* here is a parametric formula for the mean *)
 mean =Assuming[k \[Element] Integers && k ? 0,    Sum[d Log[10, 1 + 1/d], {d,
 10^k, 10^(k + 1) - 1}]] // FullSimplify
 
 (* the formula appears to be wrong *)
 Table[N[mean], {k, 0, 4}]



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