Hi I was looking at a quick way to remember converting farenheit to centigrade. It's easy to remember subtract or add 32 but then you have to multiply or divide by 1.8. I approximated this to 2. On looking at the error I saw if I added the multiplication or division by .2 it was very close to the correct answer. So I started playing with approximations of 1/(a+b). I got 1/a - b/(a^2+ab). If you do the same approximation on the last term a series starts to appear. I remember vaguely from school that was a polynomial series. I Googled Lagrange and a few others but could not find it.
Does anyone remember the approximation of 1/(x+a) as 1/x + b/x^n .....
Thanks
The approximation of $\displaystyle \frac{1}{x+a}=\frac{\frac{1}{a}}{1-(-\frac{x}{a})}=\frac{1}{a}\left(1-\frac{x}{a}+\frac{x^2}{a^2}-\frac{x^3}{a^3}... \right)$