P-Series Test

Equation
$$\sum_{n = 1}^{oo} \frac{1}{n^p}$$

Use
 Find the exponent of p as shown in the above equation.  If $$p > 1$$ the series will converge. If $$p \leq 1$$ the series will diverge. 

Explanation
A P-Series, also called a hyperharmonic series, is a modified harmonic series. When $$p = 1$$ the series is considered to be a harmonic series. When p is greater than or less than one we call the series a p-series.

Using an Integral Test we can prove that any p-series with a p value greater than 1 will converge. By using the Direct Comparison Test test with a harmonic series we can prove that any p-series with a value of p less than 1 will diverge.

Graph


Video Explanation


All Video Explanations by PatrickJMT