# P Series

### P Series

In this lesson, we will learn about p-series. They take on a special form, and look very similar to Harmonic series. However their convergence or divergence depends on the denominator's exponent, p. If p is greater than 1, then the series converge. If p is less than 1, then the series diverge. In this lesson, we will start off with looking at some simple p-series questions. Then we will look at a complicated p-series which convergences and divergences depending on a certain value.

#### Lessons

Note *P Series are in the form:
$\sum_{n=1}^{\infty}\frac{1}{n^p}$
where if $p$ > 1 then the series converge. Otherwise, the series diverges.
• Introduction
P series Overview

• 1.
Convergence and Divergence of P Series
Determine whether the series is convergent or divergent
a)
$\sum_{n=3}^{\infty}\frac{1}{n^2}$

b)
$\sum_{n=1}^{\infty}\frac{n^3+1}{n^2}$

• 2.
For what values of $k$ does the series $\sum_{n=1}^{\infty}\frac{n^3+1}{n^{(2k+1)}}$ converge and diverge?