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Power Serieshard
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The Dirichlet eta function is defined as η(s)=∑n=1∞(−1)n−1ns\eta(s) = \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^s}η(s)=∑n=1∞​ns(−1)n−1​ for s>0s > 0s>0. Consider the power series f(x)=∑n=1∞(−1)n−1xnn2f(x) = \sum_{n=1}^{\infty} \frac{(-1)^{n-1} x^n}{n^2}f(x)=∑n=1∞​n2(−1)n−1xn​ for ∣x∣≤1|x| \leq 1∣x∣≤1. What is f(1)f(1)f(1)?