Super Quick Series Classification

[airforceone]

Hi,

Quick question. Is the series below harmonic?

I ask this because I wasn't sure if the n in the p-series template (1/(n^p)) can only be a single term.

Thanks!

 

[daon]

It is neither per the definitions, but converges by comparison with a p-series. The general harmonic series diverges (power of n =1).

 

[BigGlenntheHeavy]

\(\displaystyle \frac{1}{n^{2}+1} \ < \ \frac{1}{n^{2}}, \ Comparsion \ Test.\)

\(\displaystyle And \ since \ \frac{1}{n^{2}} \ converges, \ \frac{1}{n^{2}+1} \ must \ also \ converge, \ hence \ not \ harmonic.\)

 

[airforceone]

Okay thanks guys!