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cauchysum

Run Example
(%i1)sum (2^i + i^2, i, 0, n), cauchysum;
                                 n
                                ====
                                \       i    2
(%o1)                            >    (2  + i )
                                /
                                ====
                                i = 0
(%i2) 
Run Example
cauchysum:true;
(%o1)                                true
(%i2) psexpand:multi;
(%o2)                                multi
(%i3) sumexpand:false;
(%o3)                                false
(%i4) gensumnum:0;
(%o4)                                  0
(%i5) intosum(sumcontract(sum(sum(1/((2*k)^s), k, 1, inf) + sum(1/((2*k+1)^s), k, 0, inf), s, 2,2))), simpsum;
                          inf
                          ====                      2
                          \           1          %pi
(%o5)                      >    -------------- + ----
                          /        2              24
                          ====  4 k  + 4 k + 1
                          k = 0
(%i6) 
Run Example
cauchysum:true;
(%o1)                                true
(%i2) psexpand:false;
(%o2)                                false
(%i3) simpproduct:true;
(%o3)                                true
(%i4) sumexpand:false;
(%o4)                                false
(%i5) gensumnum:1;
(%o5)                                  1
(%i6) sumcontract(intosum(sum(sum(1/((2*k)^s), k, 1, inf) + sum(1/((2*k+1)^s), k, 0, inf), s, 2,2))), simpsum;
                          inf
                          ====                      2
                          \           1          %pi
(%o6)                      >    -------------- + ----
                          /        2              24
                          ====  4 k  + 4 k + 1
                          k = 0
(%i7) 

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