Answer:
The sum is [tex]S=\frac{16}{5}=3.2[/tex]
Step-by-step explanation:
To find the sum of the infinite geometric series we must first find the common ratio r.
The series is:
4-1 + 1 / 4-1 / 16 +
[tex]r =\frac{a_{n+1}}{a_n}[/tex]
[tex]r=\frac{-1}{4}=-\frac{1}{4}\\\\r=\frac{\frac{1}{4}}{-1}=-\frac{1}{4}[/tex]
Then the common ratio r is
[tex]r=-\frac{1}{4}[/tex]
The first term is: [tex]a_1=4[/tex]
By definition when [tex]0 <| r | <1[/tex] then the sum of the infinite sequence is:
[tex]S=\frac{a_1}{1-r}\\\\S=\frac{4}{1-(-\frac{1}{4})}\\\\S=\frac{4}{\frac{5}{4}}\\\\S=\frac{16}{5}[/tex]
