Hi, I am having to expand the taylor series 1/(1-x) around the point 0.25 to 3 degrees.
I am okay expanding it around x=0 and x=.5 but for this question I am having difficulties due to the point being 0.25.
Currently I have gotten 4/3 for the first one and (16/9x - 4/9) for the 1st order.
The second order I got is (32/27)x^2 - (16/27)x + (2/27).
Due to all these extra terms being generated, I am unable to cancel out terms to make it into a geometric series. Any help would be appreciated.
If you can do it for , why would be any different?
Captain Black gives the formula for a general Taylor's series. Since you specifically mention "geometric series", you can also do it this way-
Write as .
Now divide both numerator and denominator by .75:
Now, you should be able to recognise that as with A= 4/3 and and you know that that is the sum of the geometric series .