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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why 1/n converges

**Physics Forums | Science Articles, Homework Help, Discussion**