Why the serie [tex]\sum\frac{1}{n}[/tex] diverges and the serie [tex]\sum\frac{1}{n^{2}}[/tex] converges? I'd appreciate an explanation beyond the definition of geometric series (I know that the sum of a geometric serie is given by a formula).(adsbygoogle = window.adsbygoogle || []).push({});

I've found an explanation, that involves the creation of groups in the series so each of them result 1/2 (at least), so the sum diverges. Could I apply the same operation to the sum 1/n^{2}?

thanks

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# Why 1/n converges

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