Question

Find a taylor series for (6x^2)/(1+x^3) centered around x=0

Answer 1

That just means a Maclaurin Series

Answer 2

the series would be: f(x) = f(0) + f'(0)x + 0.5f''(0)x^2 + (0.5)(0.33333)(f'''(0)x^3)... etc

Answer 3

just differentiate the equation a couple of times, and plug in x = 0 into each differential

Answer 4

I can do that but I need it in summation notation with the sigma, n=0 to infinity and all. I believe that it is \[6x^2 \sum_{n=0}^{\infty} (-x^3)^n\]but I don't know how to bring that 6x^2 inside the series. I also don't know if that is right.