unexpected behaviour of Sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg126483] unexpected behaviour of Sum*From*: perplexed <yudumbo at gmail.com>*Date*: Mon, 14 May 2012 01:34:06 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

I do not want to say that this is a bug, however I did not find, in the Sum documentation, an explanation of this behaviour (v8.0.4) I defined an innocent function like sod[n_]:=Plus@@IntegerDigits[n] that compute the sum of the digits of a number. (I tried with other functions, so the culprit is not IntegerDigits) Then I compute two sums: Sum[sod[k],{k,10^6}] which gives 27000001 (ok) then Sum[sod[k],{k,1+10^6}] which gives 500001500001 (nonsense). then Sum[sod[k],{k,2,1+10^6}] which gives 27000002 (ok) so, it seems to me that Sum has a problem when the iterator works in a range greater than 10^6. Indeed, I made an experiment: I set L={}; and defined sod[n_]:=(AppendTo[L,n];Plus@@IntegerDigits[n]) Then Sum[sod[k],{k,1+10^6}] still gives 500001500001 and at the end L is equal to {k}, so it seems that Sum tried to do something symbolic (??). Is this a bug or a feature whose documentation I was not able to find? Say, is there an option to fix things ? Btw, using ParallelSum instead of Sum works fine (and faster). thanks

**Follow-Ups**:**Re: unexpected behaviour of Sum***From:*Bob Hanlon <hanlonr357@gmail.com>

**Re: unexpected behaviour of Sum***From:*Andrzej Kozlowski <akozlowski@gmail.com>