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Sum problem


Hi ,

I have a problem that drives me crazy. In order to sum a (long) list of
elements (random numbers), say tab

tab = Table[Random[], {10^7}];

we use 

In[3]:=
Plus@@tab

Out[3]=
4.999014220610286`*^6

....but to check Sum we get

In[6]:=
Sum[tab[[i]],{i,1,Length[tab]}]

Part specification K$30 is neither an 
    integer nor a list of integers.

There is no problem for 

Sum[tab[[i]], {i, 1, 10^6}]

...and for

Sum[tab[[i]], {i, 1, 5*10^6}]

So Sum is ok. for number of elements of tab less than certain number that is
< Length[tab]

I also tested recursion methods (doSum[k_]:=doSum[k]=doSum[k-1] ...... Etc)
and got the same : fine but not for many elements (of course I set
$RecursiveLimit and $IterationLimit as Infinity)

I understand that to sum a list of elements we use Plus, Total  etc but
nevertheless I want understand what I explained above.

Best,

Arek


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