Expand f(x) = x/(x+1) in a taylor series about a=10.
f(x) = Ʃ (f^n(a)*(x-a)^n / n!
The Attempt at a Solution
I'm having a hard time arriving at the correct answer..I think I'm definitely getting lost somewhere along the way. Here's what I've got so far:
I started by computing the derivatives.
f'(x) = 1/(x+1)^2
f''(x) = (-2(x+1))/(x+1)^4
Then evaluating each at 10:
f'(10) = 1/121
f''(10) = -22/14641
and f(10) = 10/11
Then, using the above equation,
10/11 + 1/121 * (x-10) + (-22/11^4 * (x-10)^2)/2 + ....
This doesn't really take me in the right direction at all, though. I know x/1-x is near the form 1/1-x which I need for a power series expansion. Should I be trying to represent it as such?
Hope this is clear! I'm quite confused!