Answer:
A. Converges
B. geometric and the common ratio is 0.2
Given the sequence,
[tex]1000+200+40+8+\frac{8}{5}+\cdots[/tex]
we can determine whether it diverges or converges by finding the ratio of the given geometric sequence.
If:
|r| < 1, the series converges.
|r| ≥ 1, the series diverges.
We can find the ratio r by dividing a term by the previous term. For instance,
[tex]\frac{200}{1000}=0.2[/tex][tex]\frac{40}{200}=0.2[/tex][tex]\frac{8}{40}=0.2[/tex]
Now that we know that the ratio is 0.2,
[tex]|r|=|0.2|=0.2,0.2<1_{}[/tex]
This means that the series converges, and we know it because the series is geometric and the common ratio is 0.2.
