#### Mampac

##### New member

- Joined
- Nov 20, 2019

- Messages
- 42

Hello,

I managed to find the power series form for the function -- separated x

^{2}, rewrote the denominator as 1 - (-2x)

^{3}, got a power series with n running from 0 to infinity with the term (-1)

^{n}2

^{3}x

^{3n}. I pulled out the 2

^{3}as 8 and got 8x

^{2}times the power series.

For the integral, I integrated the power series by term-by-term integration and evaluated from 0 to 1/4.

Now I got some issues in b: my question is, for the remainder |R| <= a

_{n + 1}<= 10

^{-2}, should I include the 8x

^{2}in my computations?

I proceeded to write that a

_{n+1}

^{-1}=> 100, and plugged in ns, starting from 1, inside the a

_{n+1}

^{-1}.

What to do with 8x

^{2}then? Maybe I shouldn't've pulled it out of the series, or maybe after I find the S

_{n}(it turned out S

_{1}suffices since the condition was met at n = 1) I have to do additional computations?

I mean it seems like I found a value but it looks extremely suspicious.

Thank you in advance!