Word Count : 343

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To determine whether the given series \[ \sum_{n=1}^{\infty} \frac{n^2 \cdot x^5}{n^4 + x^3}, \quad x \in [0, \alpha] \] is uniformly convergent for \( x \in [0, \alpha] \), where \( \alpha \) is a positive real number, we will approach the problem using standard criteria for uniform convergence, like the Weierstrass M-test. ### Step 1: Analyze the General Term We start by analyzing the general term of __________ __________ _______ ___ ___ __________ _______ _____ ________ ______ _______.
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