Continuity check

Calculus Level 4

mm is a positive integer such that

f(x)=k=1xm(1+x4)k1. f(x) = \sum_{k=1}^\infty \frac{x^m}{(1+x^{4})^{k-1}}.

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

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