Summation and Products

 

In Mathematica

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

inputs outputs

• modul Algebra`SymbolicSum` dealing with sumation

      Needs[ "Algebra`SymbolicSum`" ]
  
      Sum[ m^2 x^m, m, 1, n ]
  

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

      Sum[ Cos[(2m-1) Pi/ (2n+1)], m,1,r ]
  

             Pi             Pi       Pi r
      -Cos[-------] + Cos[------- - -------]
           1 + 2 n        1 + 2 n   1 + 2 n
  
              Pi           Pi       Pi r
        Csc[-------] Sin[------- + -------]
            1 + 2 n      1 + 2 n   1 + 2 n

      Product[ Exp[ Sin[m x]], m, 1, n ]
  

       Csc[x/2] Sin[(n x)/2] Sin[((1 + n) x)/2]
      E

      Sum[ m 2^m/ Factorial[m+2], m,1,n]
  

          n      n
      -6 2  - 2 2  n + Gamma[4 + n]
      -----------------------------
              Gamma[4 + n]