Divergence of harmonic series

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. Why does harmonic series diverge?
?
Examples
Lessons
  1. Divergence of Harmonic Series
    Show that the following series are divergent:
    1. ∑n=2∞1n \sum_{n=2}^{\infty}\frac{1}{n}
    2. ∑n=1∞5n \sum_{n=1}^{\infty}\frac{5}{n}
    3. ∑n=1∞[n+1n2] \sum_{n=1}^{\infty}[\frac{n+1}{n^2}]
Topic Notes
?
In this section, we will talk about the divergence of Harmonic Series. A lot of people think that Harmonic Series are convergent, but it is actually divergent. We will first show a simple proof that Harmonic series are divergent. Then we will tackle some questions which involves algebraically manipulating the series to a Harmonic Series. Note that you can have several cases where some algebraic manipulation can lead to having more series. As long as you show that one of the series is Harmonic, then you can state that the entire thing is divergent.
Note *Harmonic Series are in the form:
∑n=1∞1n \sum_{n=1}^{\infty}\frac{1}{n}
It is always divergent.
Basic Concepts
?