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These are questions asked by Kitonum

Can Maple look for the limit of a sequence  f(n)  for n=1,2,3, ... ? Of course, if there is a limit of the function of continuous argument, the limit of the sequence is the same number. But it is easy to give examples of when there is the limit of the sequence, and the limit of the function does not exist:

assume(n, posint):

 limit(sin((n^2+1)/n*Pi), n=infinity);  # Obviously the correct answer is  0

                            -1 .. 1


Why does Maple 2015 solve this very simple system incorrectly?

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});



With Maple 12 no problem:

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});




In my  Standard GUI Maple 2015 (32 bit)  on Windows 8.1  plots[spacecurve]  command does not work:

plots[spacecurve]([cos(t), sin(t), t], t = 0 .. 2*Pi);



Can someone confirm this bug?

Can we output a mixed number instead of  an improper fraction in Maple programmatically. For example  

                 instead  of


The expression  expr  the command  simplify  simplifies without any problems. Even certain automatic simplification is produced:





But if we slightly modify the expression, the simplification is not performed:





The last expression  expr1  succeed to simplify the only combination of commands:




What is the reason for this strange behavior of  simplify?

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