Yesterday I was doing a WeBWork and had to check the convergence of $\sum_{n=1}^{\infty}\frac{3\ln(n)}{n^7}$; It seemed quite straight forward to me, I answered that it converges but the system told me that my answer was incorrect.
That is not the first time that this happened to me so I searched WeBWork Wiki about how does WeBWork check answers and found this:
Answer Evaluation:
When setting up the answer and solution section, we override the default answer checker in the answer. The replacement is a Perl subroutine that takes as its arguments the correct answer, student answer, and answer hash that is being processed in the answer comparison. Its return value should be $1$ if the student's answer is correct, and $0$ (false) otherwise.
When doing the relational check, you should always put the correct answer on the left and the student answer on the right, e.g.,
cos($correct) == cos($student)should be used, butcos($student) == cos($correct)should not since the relational operator works from left to right which would mean that the student's answer would be determining the settings (such as domain of function evaluation) instead of the correct answer.
I understand that the answer I enter is cos($student) but I do not know any coding so what's unclear to me is how WeBWork determines what is cos($correct) and what is not. Is it calculated by the computer or is it predetermined by the person who created the question and can a mere typo cause such problems?
My limited understanding is that there is a Maple component to the WebWorK system. To check if two numbers agree, it computes them to many decimals and compares. To check if two functions agree, it evaluates them at a few random arguments and checks if they agree. Of course the question coder has to tell the system what is considered a match. For example, when computing an indefinite integral, we allow them to differ by a constant.