Summation and Products

 

In Reduce

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

inputs outputs

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

         n  2  2      n  2      n  2      n          n      n      n
    (x*(x *n *x  - 2*x *n *x + x *n  - 2*x *n*x + 2*x *n + x *x + x  - x

                 3      2
         - 1))/(x  - 3*x  + 3*x - 1)

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

           2*r*pi
      sin(---------)
           2*n + 1
    ------------------
              pi
     2*sin(---------)
            2*n + 1

    prod(e**(sin(m*x)),m,1,n);

           cos(x/2)/(2*sin(x/2))
          e
    ----------------------------------
      cos((2*n*x + x)/2)/(2*sin(x/2))
     e

    for all n,m such that fixp m let
            factorial(n+m)=if m > 0 then factorial(n+m-1)*(n+m)
                       else factorial(n+m+1)/(n+m+1);

    sum(m*2**m/factorial(m+2),m,1,n);

           n                 2
      - 2*2  + factorial(n)*n  + 3*factorial(n)*n + 2*factorial(n)
    ---------------------------------------------------------------
                                     2
                      factorial(n)*(n  + 3*n + 2)