Word Count : 258

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To prove that the series \[ \sum_{n=1}^{\infty} n^3 X^n \] converges uniformly on the interval \(\left[ -\frac{1}{3}, \frac{1}{3} \right]\) using the Weierstrass M-test, we need to find a sequence of functions \(M_n\) such that: 1. \(|f_n(x)| \leq M_n\) for all \(x \in \left[ _______ _____ _________ _________ __________ __________.
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