Using Weiestrass M-test, show that the following series converges uniformly.
Consider the series (\sum_{n=1}^{\infty} n^3 x^n) for (x \in \left[-\frac{1}{3}, \frac{1}{3}\right]). To apply the Weierstrass M-test, we need a sequence of constants (M_n) such that (|n^3 x^n| \le M_n) for all (x) in the interval and (\sum M_n) converges. ___ ___ ___ ___ __________ ______ _________ ___ __________ _______ _________ ___.
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(i)
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