# Taylor series problem

• May 27th 2009, 10:59 AM
Sniperpro
Taylor series problem
ive been stuck on the following question and dont really know what to do:

Consider the function $\displaystyle f(x)= 1/(1+x)$ about x=0

Find the third Taylor polynomial p3(x) and express the taylor series. (Include an expression for the general term of the series)

its difficult to get the third taylor polynomial because it leads to calculating things divided by zero which is impossble.
• May 27th 2009, 11:20 AM
apcalculus
Quote:

Originally Posted by Sniperpro
ive been stuck on the following question and dont really know what to do:

Consider the function $\displaystyle f(x)= 1/(1+x)$ about x=0

Find the third Taylor polynomial p3(x) and express the taylor series. (Include an expression for the general term of the series)

its difficult to get the third taylor polynomial because it leads to calculating things divided by zero which is impossble.

First derivative is: $\displaystyle \frac{-1}{(1+x)^2}$
Second Derivative is: $\displaystyle \frac{2}{(1+x)^3}$
Third Derivative is is: $\displaystyle \frac{-6}{(1+x)^4}$
...

As you see, when you evaluate the derivative at x=0 you never end up dividing by zero. Good luck!!