Example 6.4.11
Let's apply the root test to
We have
Thus the root test tells us exactly what we already know about
convergence of the geometry series (except when
![$ \vert r\vert=1$](img1152.png)
).
Example 6.4.15
Consider
![$ \sum_{n=1}^{\infty} \frac{n^n}{3\cdot (27^n)}$](img1158.png)
.
To apply the root test, we compute
Again, the limit diverges, as in Example
6.4.8.