       Re: unexpected behaviour of Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg126500] Re: unexpected behaviour of Sum
• From: Dana DeLouis <ng201005 at me.com>
• Date: Tue, 15 May 2012 04:53:57 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```> Sum[sod[k],{k,1+10^6}] which gives 500001500001 (nonsense).

Hi.  I don't have an answer, but the nonsense number looks to me like it skipped the function, and just added the Ks

1/2 n (1+n) /.n -> 1+10^6
500001500001

Don't have an answer, but bypassing the function seems to work.

Sum[Plus@@IntegerDigits[j],{j,1+10^6}]
27000003

Just interesting:

digits 0 thru 9 sum to 45.

1/2 n (1+n) /. n->9
45

Sum of digits 1 thru 999,999 might be:

{100000,100000,100000,100000,100000,100000}.{45,45,45,45,45,45}
27000000

Reducing to:

100000*(6*45)
27000000

Sum[Plus@@IntegerDigits[j],{j,10^6,1+10^6}]
3

%% + %
27000003

This gave an interesting alternative for a closed form...

z=Table[Power[10,j-1]*(j*45),{j,1,8}]
{45,900,13500,180000,2250000,27000000,315000000,3600000000}

FindSequenceFunction[z,n]
9 2^(-1+n) 5^n n

Which matched here:

WolframAlpha[ToString[z]]
<< . . . >>

Also of interest:
http://oeis.org/A034967

= = = = = = = = = =
HTH  :>)
Dana DeLouis
Mac & Math 8
= = = = = = = = = =

On May 13, 10:34 pm, perplexed <yudu... at gmail.com> wrote:
> 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

```

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