(8) \((10\%)\) Let \(f{n}:[0,1]\to \mathbb{R}\) be defined by \(f{n}(x) = \frac{x^{2}}{(1 + x^{2})^{n}}\)

(a) Prove that \(\sum{n=1}^{\infty} fn(x)\) is convergent for \(x \in [0,1]\).