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