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Uniform convergence
Uniform convergence
Prove that the series of functions $\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^3 x^2 + n}$ converges uniformly for all $x \geq 0$.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$