Again stuck on this stuff.
I swear I had the right answer... 4 times in a row... and now I'm stuck with one attempt left and i'm afraid to try again
I think what I am doing wrong, is I am missing the part of the pattern where the numerator is multiplied by -7.
I think my answer should be reflecting that each time, it is being multiplied by -1, -2, -6, -24, but I don't know how to show this in my series.
Hint
You can simplify the problem setting $x=y+a$. So $$f=\frac 7 x=\frac 7 {y+a}=\frac 7a \frac{1}{1+\frac y a}$$ Now, let $z=\frac y a$ which make $$f=\frac 7a \frac{1}{1+z}$$ Now, remember that $$\frac{1}{1+z}=\sum_{n=0}^\infty (-1)^n z^n$$ Go back to $y$ and then to $x$.
I am sure that you can take it from here.