Use this list of basic taylor series to find the taylor series for f(x) = 2x 1+x2 based at 0. give your answer using summation notation and give the largest open interval on which the series converges. (if you need to enter ∞ , use the ∞ button in calcpad or type "infinity" in all lower-case.) the taylor series for f(x)= 2x 1+x2 is: ∞ k=0 the taylor series converges to f(x) for |x|< . use the taylor series you just found for f(x)= 2x 1+x2 to find the taylor series for ln(1+x2) based at 0. give your answer using summation notation and give the largest open interval on which the series converges. the taylor series for ln(1+x2) is: ∞ k=0 the taylor series converges to ln(1+x2) for |x|< .