Question: How can I force Maple to rewrite expressions containing Sum?

Hi,

Is it possible to force Maple to simplify these Sum(s) ?
SimplifySum.mw
 

s := Sum(a*X[n]+b, n=1..N);
simplify(s);
value(s);  # part of the job done  but...


IWouldLikeToHave = a*Sum(X[n], n=1..N) + b*N; # or +N*b, it doesn't matter

Sum(a*X[n]+b, n = 1 .. N)

 

Sum(a*X[n]+b, n = 1 .. N)

 

N*b+sum(a*X[n], n = 1 .. N)

 

IWouldLikeToHave = a*(Sum(X[n], n = 1 .. N))+N*b

(1)

s := Sum(X[n]+Y[n], n=1..N);
(expand@value)(s);


IWouldLikeToHave = Sum(X[n], n=1..N) + Sum(Y[n], n=1..N);

Sum(X[n]+Y[n], n = 1 .. N)

 

sum(X[n]+Y[n], n = 1 .. N)

 

IWouldLikeToHave = Sum(X[n], n = 1 .. N)+Sum(Y[n], n = 1 .. N)

(2)

 

 

 

Thanks in advance

 

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