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Infinite Serieshard
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Using Parseval's identity and the Fourier series of f(x)=x2f(x) = x^2f(x)=x2 on [−π,π][-\pi, \pi][−π,π], which is x2=π23+4∑n=1∞(−1)nn2cos⁡(nx)x^2 = \frac{\pi^2}{3} + 4 \sum_{n=1}^{\infty} \frac{(-1)^n}{n^2} \cos(nx)x2=3π2​+4∑n=1∞​n2(−1)n​cos(nx), find the value of ∑n=1∞1n4\sum_{n=1}^{\infty} \frac{1}{n^4}∑n=1∞​n41​.