The question asks me to write out a taylor polynomial for 1/(1-x^2)
of degree 2n+1 at 0.
The Attempt at a Solution
My answer was 1 + x^2 + x^4 + x^6 + ..... + (x^4)/(1-x^2) which I just got from using hte geometric series formula. The textbook answer however is this:
1 - x^2 + x^4 - ............. + (-1)^n x^2n
Am I wrong? I thought so, but I took out a graphing calculator, and the larger I make my polynomial degree, the closer it looks to 1/(1-x^2). So my answer must be correct?