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Infinite Seriesmedium
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For the series ∑n=1∞1n2\sum_{n=1}^{\infty} \frac{1}{n^2}∑n=1∞​n21​ which converges to π26\frac{\pi^2}{6}6π2​, use the Integral Test to bound the remainder RN=∑n=N+1∞1n2R_N = \sum_{n=N+1}^{\infty} \frac{1}{n^2}RN​=∑n=N+1∞​n21​.