I need to find the first three nonzero terms of the Maclaurin series (so generated at $x=0$) and the values of x for which the series converges absolutely
$$f(x)=\frac {x^3}{1+2x}$$
So I found the first 3 nonzeros which are $f'''(0)=6$, $f^4(0)=-48$, and $f^5(0)=480$
So $$f(x)={x^3}-{2x^4}+{4x^5}-{8x^6}+{16x^7}$$ I added a few more terms to help the pattern.
How do I find the series from this and find the values of x for which the series converges absolutely? Thank you for the help
The solution in three steps as shown above