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Infinite Seriesmedium
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For the series ∑n=1∞1n3\sum_{n=1}^{\infty} \frac{1}{n^3}∑n=1∞​n31​, estimate the error when approximating the sum using the first 10 terms. Use the Integral Test remainder bound: R10≤∫10∞1x3dxR_{10} \le \int_{10}^{\infty} \frac{1}{x^3} dxR10​≤∫10∞​x31​dx.