Environment for creative processing of text and numerical data

Comparing sums of powers and Riemann's zeta function

Beginning status (before activation):

   1 *
   2 *sum(N):=for(i=1)to(N)sum(1/i^2) sum2(N):=for(i=1)to(N)sum(1/i^2+1/N/N)
   3 *                                better approximation with a small correction
   4 *    sum(10).=                        sum2(10).=
   5 *   sum(100).=                       sum2(100).=
   6 *  sum(1000).=                      sum2(1000).=
   7 * sum(10000).=                     sum2(10000).=
   8 *sum(100000).=                    sum2(100000).=
   9 *    zeta(2).=                         zeta(2).=
  10 *
  11 *pi=3.141592653589793
  12 *pi^2/6-zeta(2).=  
  13 *

Ending status (after activation):

   1 *
   2 *sum(N):=for(i=1)to(N)sum(1/i^2) sum2(N):=for(i=1)to(N)sum(1/i^2+1/N/N)
   3 *                                better approximation with a small correction
   4 *    sum(10).=1.5497677311665         sum2(10).=1.6497677311665
   5 *   sum(100).=1.6349839001849        sum2(100).=1.6449839001849
   6 *  sum(1000).=1.6439345666816       sum2(1000).=1.6449345666816
   7 * sum(10000).=1.6448340718481      sum2(10000).=1.6449340718481
   8 *sum(100000).=1.6449240668982     sum2(100000).=1.6449340668982
   9 *    zeta(2).=1.6449340668482          zeta(2).=1.6449340668482
  10 *
  11 *pi=3.141592653589793
  12 *pi^2/6-zeta(2).=0 
  13 *

This is an example of simultaneous activation (all results in one).

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