Continuity check

Calculus Level 4

\(m\) is a positive integer such that

\[ f(x) = \sum_{k=1}^\infty \frac{x^m}{(1+x^{4})^{k-1}}. \]

Given that \( f(x) \) is continuous at \( x = 0\), find the smallest possible value of \(m \).

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