For what values of \(\alpha\) the series \(\displaystyle\sum_{n=1}^{N} \frac{1}{n^\alpha}\) diverges as \(N \to \infty\)?
Divergence of the $p$-series $\sum n^{-\alpha}$
P-TRIV-RA52
- Area
- Real Analysis
- Status
- draft
P-TRIV-RA52
For what values of \(\alpha\) the series \(\displaystyle\sum_{n=1}^{N} \frac{1}{n^\alpha}\) diverges as \(N \to \infty\)?