題組內容
(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 \( x \in [0,1] \).
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(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 \( x \in [0,1] \).