Zadanie 12b, Paper 2, maj 2025, TZ1, Matematyka AA IB HL

For nonnegative integers n, let $F_n(x)=\sum_{r=0}^n\left(\frac{1-x^2}{2}\right)^r$. Define $F(x)=\lim_{n\to\infty}F_n(x)$ wherever the limit exists. Let K be the largest positive number for which convergence holds throughout (−K, K), and define g(x) = F(x) for 0 ≤ x < K.