Summation and Products

 

In Macsyma

For comparison with other CAS choose from: Axiom Derive Maple Mathematica Reduce

inputs outputs

    load(nusum1)$

    closedform(sum(m^2*x^m, m, 1, n));

         n + 1   2  2         2                 2
        x      (n  x  + (- 2 n  - 2 n + 1) x + n  + 2 n + 1)   x (x + 1)
        ---------------------------------------------------- - ---------
                                     3                                3
                              (x - 1)                          (x - 1)

    closedform(sum(cos((2*m-1)*%pi/(2*n+1)), m, 1, r));

                             r
                            ====
                            \         %pi (2 m - 1)
                             >    cos(-------------)
                            /            2 n + 1
                            ====
                            m = 1

    closedform(product(%e^(sin(m*x)), m, 1, n));

                                                       %i n x + %i x
                               %i                 %i %e
      expt(%e, - ------------------------------ - ------------------
                     %i n x + %i x       %i n x          %i x
                 2 %e              - 2 %e            2 %e     - 2

                                                     %i x
                                                %i %e              %i
                                             + ------------ + ------------)
                                                   %i x           %i x
                                               2 %e     - 2   2 %e     - 2

    closedform(sum(m*2^m/(m+2)!, m, 1, n));

                                      n
                                   2 2
                             1 - --------
                                 (n + 2)!