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Math · Advanced Math
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Prove that the p-series converges when p=2 without using the Integral Test. Hint: Let 51 denote the th partial sum of the harmonic series, verify that フ2 for each n, and then explain why this shows that the series does not converge. For the case in which P=2, use 1/(k2 -k) as an overestimate of 1/k^2 for all k > 1, then show that the partial sums of this larger series (with the sum starting at k=2) are bounded above by 1.

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