Ononot — Let fn(x) = \frac{x^n}{1 + x^{2n}} for x \in \mathbb{R}. For

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Infinite Serieshard

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Let $f_n(x) = \frac{x^n}{1 + x^{2n}}$ for $x \in \mathbb{R}$ . For which of the following intervals $I$ does the series of functions $\sum_{n=1}^{\infty} f_n(x)$ converge uniformly on $I$ by the Weierstrass M-test?