Answer
Oscillates and converges
Work Step by Step
The general form of geometric series is written as:
$\Sigma_{n=0}^{\infty} ar^n=a+ar+ar^2+ar^3+.......=\dfrac{a}{1-r}~~~~(1)$
when $|r| \lt 1$, then the sequence converges.
Here, we are given the geometric series $100 (-0.003)^{n}$
On comparing the above equation with the equation (1), we get
$a=100$ and $r=-0.003$
This implies that the common ratio $|r|=0.003 \lt 1$ , so the sequence converges.
Hence, we conclude that the sequence increase and decrease and the every term of the sequence shows an alternate pattern. This means that the given sequence oscillates and converges.
