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simpsum-sum

S1 : sum( k , k , 1 ,...

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simpsum-sum

x:2.5;

sum((k+x)^2, k, 1, 12...

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simpsum-sum

c(x, y):= x!/(y!*(x-y...

d(a, b, o, t):= sum((...

d(8,9,3,2);

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simpsum-sum

sum(n-i,i,0,n), simpsum;

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simpsum-sum

sum(k^2, k, 1, 25), s...

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simpsum-sum

sum(1/k^2,k,1,100),si...

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simpsum-sum

sum (2^i + i^2, i, 0,...

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simpsum-sum

sum(n/1,n,inf,1), sim...

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simpsum-sum

sum(n-i,i,0,n), simpsum;

Calculate

simpsum-true

simpsum:true;

sum(a[n]=a[n-1]+a[n-1...

simpsum;

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simpsum

Run Example
(%i1)f:1/(1+x);
                                       1
(%o1)                                -----
                                     x + 1
(%i2) s(n,x):=integrate((-x)^n,x,0,1);
                                               n
(%o2)                s(n, x) := integrate((- x) , x, 0, 1)
(%i3) s(0,x);
(%o3)                                  1
(%i4) s(1,x);
                                        1
(%o4)                                 - -
                                        2
(%i5) s(2,x);
                                       1
(%o5)                                  -
                                       3
(%i6) s(3,x);
                                        1
(%o6)                                 - -
                                        4
(%i7) g3:sum((-x)^k,k,0,3);
                                  3    2
(%o7)                          - x  + x  - x + 1
(%i8) g:sum((-x)^k,k,0,n-1),simpsum;
                                       n
                                  (- x)  - 1
(%o8)                             ----------
                                   - x - 1
(%i9) S3:integrate(g3,x,0,1);
                                      7
(%o9)                                 --
                                      12
(%i10) fmg:f-g;
                                           n
                                1     (- x)  - 1
(%o10)                        ----- - ----------
                              x + 1    - x - 1
(%i11) fmg:factor(fmg);
                                         n
                                    (- x)
(%o11)                              ------
                                    x + 1
(%i12) 
Run Example
? simpsum;

 -- Option variable: simpsum
     Default value: `false'

     When `simpsum' is `true', the result of a `sum' is simplified.
     This simplification may sometimes be able to produce a closed
     form.  If `simpsum' is `false' or if the quoted form `'sum' is
     used, the value is a sum noun form which is a representation of
     the sigma notation used in mathematics.


(%o1)                                true
(%i2) 
Run Example
declare(sum,additive);
(%o1)                                done
(%i2) v:sum(1/n^3,n,1,inf),simpsum;
(%o2)                               zeta(3)
(%i3) 
[abs,plot2d,simpsum,sin,sum] [additive,declare,inf,simpsum] [assume,binomial,simpsum] [assume,inf,simpsum] [augcoefmatrix,coefmatrix,col,load,matrix,simpsum,sum] [binomial,cos,factor,load,next_prime,plot2d,prev_prime,simpsum,sin,sqrt,sum,true] [binomial,cos,factor,load,next_prime,prev_prime,simpsum,sin,sqrt,sum,true] [binomial,simpsum,subst,sum] [binomial,simpsum,sum,true] [binomial,simpsum,sum] [binomial,simpsum,true] [binomial,simpsum] [cauchysum,false,gensumnum,inf,intosum,psexpand,simpsum,sumcontract,sumexpand,true] [cauchysum,false,gensumnum,inf,intosum,simpsum,sumcontract,sumexpand,true] [cauchysum,false,intosum,simpsum,sum,sumcontract,sumexpand,true] [cos,inf,simpsum,sum] [cos,simpsum,sum] [debugmode,simpsum,sum,true] [diff,factor,inf,limit,simpsum,subst,sum] [diff,factor,simpsum,subst,sum] [diff,simpsum,sum] [ev,makelist,simpsum,sum] [expand,factor,product,simpsum,true] [expand,simpsum,sum] [factor,inf,makelist,numer,powerdisp,simpsum,sum,sumcontract,true] [factor,inf,makelist,numer,powerdisp,simpsum,sum,true] [factor,inf,simpsum,sum] [factor,integrate,simpsum,sum] [factor,simpsum,sum] [factorsum,simpsum,sum] [false,simpsum,sum] [false,simpsum] [float,inf,simpsum,sum] [fullratsimp,inf,integrate,limit,simpsum,true] [gensumnum,inf,simpsum] [inf,integrate,linenum,simpsum,sum] [inf,integrate,simpsum,sum] [inf,linsolve,simpsum,sum] [inf,makelist,numer,powerdisp,simpsum,sum,true] [inf,simpsum,sum] [inf,simpsum,true] [inf,simpsum] [intosum,simpsum,sum,sumcontract] [simpsum,sqrt,sum,true] [simpsum,sqrt,sum] [simpsum,sum,sumcontract] [simpsum,sum,true] [simpsum,sum] [simpsum,true] [simpsum]

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