Re: Series and number of terms

From: S. Enterprize Company (smart1234_at_aol.com)
Date: 10/23/04 

Date: 23 Oct 2004 11:02:54 GMT

>On 22 Oct 2004 15:46:02 -0700, D wrote:
>> A fellow posed this question to me a few days ago. So far, none of my
>> professors or colleagues could answer this:
>
>> SUM(1/n^2) as n=1 to infinity.
>
>> How many terms are needed to come to a solution with an error < 0.001.
>
>> My initial thought was to integrate the p-series from 1 to k of the
>> function subtracted from the integral of the function from (k+1) to
>> infinity. Therefore, subtracting the errors should yield the term. I
>> was wrong, or did the calculations incorrectly.
>
>> I'm dying of curiousity on this one. Thanks in advance
>
>> Daniel Lausevic
>
>Mathematica says the first 1000 terms are close enough.
>
>In[1]:= NSum[1/n^2,{n,1001,Infinity}]
>
>Out[1]= 0.0009995
>
>
>
>--
>Dave Seaman
>Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
><http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
>
>
>

  A simple way I view it....

   Accuracy looks like common sense to me. You can only be as accurate as the
number of accurate values used.

If you want an accuracy of < .001, use 1000 accurate values. The inverse of
.001 = 1000

If you want an accuracy of <.0000000000001 then use 1/ (1 X10^13) 10^13
accurate terms.

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