>> I'm no mathematician, but to do that you must make the assumption that
>> there are an even number of terms in the infinite sum (ie every +1 has a
>> -1 to pair with it). You could have assumed an odd number of terms and
>> got a sum of 1 instead.
>
>> Writing the sum equals 1 minus the sum seems to avoid the need to make
>> such an assumption.
>
> An infinite sum can't have an "odd" or an "even" number of terms.

Yes that was my point, "grouping" in any way is invalid because you must 
make assumptions about the total number of terms, which you can't for an 
infinite list.

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