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sumcontract

sumcontract((x*10^y-x...

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sumcontract

? sumcontract;

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sumcontract-true

sumcontract:true;

sum(x*y*(x+y),x,1,100);

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sumcontract

sumcontract((x*10^y-x...

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sumcontract

? sumcontract;

Calculate

sumcontract-true

sumcontract:true;

sum(x*y*(x+y),x,1,100);

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sumcontract

Run Example
(%i1)2/(1-2);
(%o1)                                 - 2
(%i2) 3/(1-3);
                                        3
(%o2)                                 - -
                                        2
(%i3) 4/(1-4);
                                        4
(%o3)                                 - -
                                        3
(%i4) 5/(1-5);
                                        5
(%o4)                                 - -
                                        4
(%i5) 6/(1-6);
                                        6
(%o5)                                 - -
                                        5
(%i6) x/(1-x);
                                       x
(%o6)                                -----
                                     1 - x
(%i7) (x/(1-x)), simplify;
                                       x
(%o7)                                -----
                                     1 - x
(%i8) (x/(1-x)), factor;
                                        x
(%o8)                               - -----
                                      x - 1
(%i9) (x/(1-x)), expand;
                                       x
(%o9)                                -----
                                     1 - x
(%i10) (x/(1-x)), radcan;
                                        x
(%o10)                              - -----
                                      x - 1
(%i11) (2/(1-2*x) - 1/(1-x));
                                   2        1
(%o11)                          ------- - -----
                                1 - 2 x   1 - x
(%i12) (2/(1-2*x) - 1/(1-x)), expand;
                                   2        1
(%o12)                          ------- - -----
                                1 - 2 x   1 - x
(%i13) (2/(1-2*x) - 1/(1-x)), radexpand;
                                   2        1
(%o13)                          ------- - -----
                                1 - 2 x   1 - x
(%i14) (2/(1-2*x) - 1/(1-x)), factor;
                                       1
(%o14)                         -----------------
                               (x - 1) (2 x - 1)
(%i15) (2/(1-2*x) - 1/(1-x)), radcan;
                                      1
(%o15)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i16) x*(2/(1-2*x) - 1/(1-x)), factor;
                                       x
(%o16)                         -----------------
                               (x - 1) (2 x - 1)
(%i17) x*(2/(1-2*x) - 1/(1-x)), radcan;
                                      x
(%o17)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i18) x*(2/(1-2*x) - 1/(1-x)), expand;
                                  2 x       x
(%o18)                          ------- - -----
                                1 - 2 x   1 - x
(%i19) x*(2/(1-2*x) - 1/(1-x)), radexpand;
                                  2        1
(%o19)                        (------- - -----) x
                               1 - 2 x   1 - x
(%i20) x*(2/(1-2*x) - 1/(1-x)), simplify;
                                  2        1
(%o20)                        (------- - -----) x
                               1 - 2 x   1 - x
(%i21) y : (2/(1-2*x) - 1/(1-x)),radcan;
                                      1
(%o21)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i22) sum(y, y, 1, 3);
(%o22)                                 6
(%i23) sumcontract(y);
                                      1
(%o23)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i24) taylor(y);
                                  1
(%o24)/T/                   -------------- + . . .
                               2
                            2 x  - 3 x + 1
(%i25) taylor(x*y);
                                  x
(%o25)/T/                   -------------- + . . .
                               2
                            2 x  - 3 x + 1
(%i26) taylor(x*y), radcan;
                                      x
(%o26)                          --------------
                                   2
                                2 x  - 3 x + 1
(%i27) 
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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