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Power Serieshard
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Consider the power series f(x)=∑n=1∞(−1)nnxnf(x) = \sum_{n=1}^{\infty} \frac{(-1)^n}{n} x^nf(x)=∑n=1∞​n(−1)n​xn, which converges for ∣x∣<1|x| < 1∣x∣<1. The alternating series ∑n=1∞(−1)nn\sum_{n=1}^{\infty} \frac{(-1)^n}{n}∑n=1∞​n(−1)n​ converges by the alternating series test. By Abel's Theorem, what must be true?