# How do you do the taylor series for expanding #1/(2+x^2)#, about a = 0 up to order n = 2?

##### 1 Answer

Firstly we would find the Taylor series for the function centered at a=0, thus moreso finding is Maclaurin series.

we can make use of the common Maclaurin series of:

Now lets try and write our function to look similar to the common Maclaurin Series:

now we can just substitute

which can simplify a bit:

Now to get the expansion up to order n=2, we just follow the sum and get:

which can simplify to:

*note that this series is only convergent at #abs(x^2/2) < 1#*

thus: