I have the function f(x) = $\dfrac{2x}{\left(x-5\right)^2}$, and I'm supposed to "find the first five non-zero terms of power series representation centered at x = 0."
Using $\frac{f^{(n)}(0)}{n!}$, the first non-zero terms I get are:
C1 = 2/25
C2 = 4/125
C3 = 6/625
C4 = 8/3125
C5 = 2/3125
However, WebWork marks these as incorrect. Any alternative methods or corrections to the work above are gladly appreciated.
Best Answer
Remember, this an online system. Each of your coefficients is correct but perhaps you are missing the variables. For instance, the first term is $2x/25$ not its coefficients (because there can be constant terms in a Taylor Series). Similarly, the second term is $4x^2/125$, and so forth.
It could also be because it wants the coefficients of the terms but in order of powers, so it would $0$, $2/25$, $4/125$, etc. Though this seems less like than the first.
Overall, this seems less an issue of the mathematics - as your terms are correct, as it does how you are entering it or with the system itself. Just send a quick email to your instructor! They can see the solutions and thus perhaps more quickly tell what is incorrect about how the system wants the answer. As an instructor, I always found WebWork/WebAssign to be a bit wonky from time to time.