There is a minor anomaly with the pizza problem. I wonder if MapleTA can resolve it. I repeat the problem here for convenience.

A group of 11 male and 13 female students is planning to go out for pizza. If 82% of the male students go and 62% of the female students go, find the probability that a random student who goes out for pizza is female.

The "expected" answer, judging from the multiple-choice answers, is

(.62*13)/(.62*13+.82*11) = 0.4719.

However, the realistic answer uses a whole number of males (.82*11 = 9) and females (.62*13 = 8) and is thus

8/(8+9) = 0.4706,

which is not one of the choices. Can MapleTA automatically adjust the answers to reflect this? It would just involve using Maple's round function. This anomaly also illustrates the inherent problem of requiring more significant digits in the answer (4 sig. digits) than were provided in the problem data (2 sig. digits).

I also wonder if MapleTA was used to include the drawing of the pizza to the right of the problem.

You may have a problem displaying 3d plots. Try this:

plot3d(0, x= 0..1, y= 0..1, axes= boxed);

@Preben Alsholm 

This avoids the step of having to substitute z = exp(2*I*x).

S:= -ln(2)+Sum((-1)^(n+1)/n*cos(2*n*x), n= 1..infinity);

expand(simplify(evalc(Re(value(S))))) assuming cos(x) > 0;

Make sure you also change pi to Pi. This is necessary in Maple in order for it to interpret the symbol as the mathematical constant.

@ecterrab Note that the OP wanted a real and b imaginary.

What input gives you the error message in your title, "too many levels of recursion"?

@ecterrab Sure, I would've rather used dchange than the seemingly artificial hack of switching to integrals. But it seems that as it's currently implemented, expand does not work on Sums, even though there is an `expand/Sum`.

@sharena2 The command (in the last line) should be plot, not plots.

@mehdi jafari The problem is that the symbolic sum returned by the symbolic integration is wrong.

@lemelinm Yes, I got that plot. But I don't see the connection between that plot and the plot in your original Question.

@itsme The bug is not in the numeric summation. You can replace the infinity upper limit of summation with a finite value to show that the numeric summation is correct.

Please post your actual code. The parametric curve expression that you gave is not at all like the plot in your Question. This is the plot of the curve that you gave:

@vidocq wrote:

I have exported second file to mpl and tried read "file.mpl" but it was not work.

No. Export the first file to .mpl and place the read command at the beginning of the second file.

@dena I'm using Maple 18 also.

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@dena Preben's code works for me. You should post your executed code so that we can diagnose what you are doing wrong. Here's my worksheet of it:

Download dsolve.mw