Answer:
Converge
Step-by-step explanation:
Given geometric series
[tex]1,000+200+40+8+\dfrac{8}{5}+...[/tex]
The first term of this geometric series is [tex]a_1=1,000.[/tex]
Next terms can be obtained by dividing by 5 or multiplying by [tex]\frac{1}{5}:[/tex]
[tex]a_2=1,000\cdot \dfrac{1}{5}=200\\ \\a_3=200\cdot \dfrac{1}{5}=40\\ \\a_4=40\cdot \dfrac{1}{5}=8\\ \\a_5=8\cdot \dfrac{1}{5}=\dfrac{8}{5}\\ \\...[/tex]
The sum of this infinite geometric series is
[tex]S=\dfrac{a_1}{1-q}=\dfrac{1,000}{1-\frac{1}{5}}=\dfrac{1,000}{\frac{4}{5}}=1,250[/tex]
Hence, this series is convergent
