Answer:
Converges to 2100
Step-by-step explanation:
This is comparable to:
[tex]\sum_{k=1}^\infty a \cdot r^{k-1}[/tex] where:
r is the common ratio and [tex]a[/tex] is the first term.
The series converges to:
[tex]\text{First term}\cdot \frac{1}{1-\text{common ratio}}[/tex]
if the ratio's absolute value is less than 1.
This is a geometric series.
The common ration is .8 .
The first term in the series is 420.
Since the |.8|<1, then the series converges to a sum.
The formula for finding the sum is:
[tex]\text{First term}\cdot \frac{1}{1-\text{common ratio}}[/tex]
Plugging in our numbers:
[tex]420\cdot \frac{1}{1-.8}[/tex]
[tex]420\cdot \frac{1}{.2}[/tex]
[tex]420\cdot 5[/tex]
2100
