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Discuss the convergence or divergence of the series \sum _{{n=1}}^{{\infty }}{\frac  {1}{n}} and \sum _{{n=1}}^{{\infty }}{\frac  {1}{n^{2}}}.
The terms go to 0 for both of these series so the nth term test tells us nothing. The first series, \sum _{{n=1}}^{{\infty }}{\frac  {1}{n}}, diverges by the integral test (which we have not learned at this point) and the second series, \sum _{{n=1}}^{{\infty }}{\frac  {1}{n^{2}}}, converges also by the integral test. Thus, if the terms go to 0, we know nothing about whether or not the series converges.

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