Binomial expansion:
(1+x2)-1=1+(-1)x2+(-1)(-2)x4/2!+(-1)(-2)(-3)x6/3!+...+(-1)nn!x2n/n!=
1-x2+x4-x6+...
If x=1, we get 1-1+1-1+... which is either 0 or 1, so is indeterminate as a series. However, if x<1, the sum of this geometric progression is:
1/(1+x2), the original function. As x→1 the limit is ½. When x≥1 the sum is indeterminate or is infinite.