Question

Let y_n(x) = x² + x²/(1 + x²) + x²/(1 + x²)² + ..... + x²/(1 + x²)^{n - 1} and y(x) = lim_(n →∞) y_n(x) Discuss the continuity of y_n(x) (n ∈ N) and y(x) at x = 0

Answer 1

y_n(x) = (1 + x³){1 - (1 + x²)^-n}