What is an Infinite Series?
An infinite series is a sum of an infinite set of terms.
In an infinite series, we typically write it as:
Divergence and Convergence of an Infinite Series
Suppose that we have the infinite series:
If we try to evaluate the series for a finite amount of terms, for example, when
We see that the upon adding just the first
- We see that when we consider more terms (above
), we can see that it is much closer to .
| 15 | |
| 20 | |
| 25 | |
| 30 | |
| 35 |
Therefore, we can say that the infinite series converges to
However, if we try to consider the infinite series:
We can see that as we add more and more terms: