Answer:
converges to 2.5
Step-by-step explanation:
Given is a series as
2 + 0.4 + 0.08 + 0.016 +...
We find comparing terms that each term is multiplied by 0.2 to get the successive term
In other words, this is a geometric series infinite with common ratio = 0.2
Since common ratio <1 we find that this series converges
Sum of infinite terms of a geometric series = [tex]\frac{a}{1-r}[/tex], where a=I term and r = common ratio
Here we find that a =2, and r = 0.2
So converges to sum = [tex]\frac{2}{1-0.2} =2.5[/tex]
