The harmonic series $\sum \frac{1}{n}$ diverges.We can form a new series from the difference between consecutive terms of the harmonic series obtaining $\sum\left[\frac{1}{n+1}-\frac{1}{n}\right]$ . This series also diverges.

Question

Quizplus · Accepted Answer

The series $\sum\left[\frac{1}{n+1}-\frac{1}{n}\right]$ simplifies to $\sum\left[-\frac{1}{n(n+1)}\right]$, which is a telescoping series and converges to a finite value.

The Harmonic Series ∑1n\sum \frac{1}{n}∑n1​ DivergesWe Can Form a New Series from the Difference Between

The Harmonic Series $\sum \frac{1}{n}$ DivergesWe Can Form a New Series from the Difference Between