AP Calculus BC / Unit 10: Infinite Sequences and Series
10.5 Harmonic Series and p-Series
Notes
$$\sum\frac{1}{n^p}\ \text{converges if } p>1,\ \text{diverges if } p\le1$$
- The harmonic series $\displaystyle \sum\frac{1}{n}$ ($p=1$) diverges.
Practice
$\displaystyle \sum\frac{1}{n^{1.01}}$:
$p>1$.
$\displaystyle \sum\frac{1}{\sqrt n}$:
$\displaystyle p=\frac{1}{2}\le1$.
The harmonic series:
It grows like $\ln n$.
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