Re: Evaluating a series

[Martin Helm]

Am 09.08.2012 09:30, schrieb Søren Hauberg:
> On Aug 9, 2012, at 9:22 AM, address@hidden wrote:
>
>> Please assist me to do this:
>> Evaluate the series
>>
>> 1-1/3+1/5-1/7+1/9-...+1/1001
> You can get the positive part of the sequence by doing something like
>
>   1 ./ (1:4:1001)
>
> summing that will give you part of your result. You can do the same for the 
> negative part and subtract that from the positive part.
>
> Søren
>
I have not thought very deeply about it, but wouldn't it be more stable
to group every pair of differences together
1/n - 1/(n+2) = 2/( n*(n+2) ) so that only positive numbers are summed
and no subtractions take place?
Just a thought without details, since that sounds like homework somehow
(i also matters in which order the summation is done, not really for
this small example).