Answer:
5.33
Step-by-step explanation:
The n th term of a geometric series is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
4[tex](\frac{1}{4}) ^{n-1}[/tex] ← is the n th term of a geometric series
with a = 4 and r = [tex]\frac{1}{4}[/tex]
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a(1-r^{n}) }{1-r}[/tex], thus
[tex]S_{10}[/tex] = [tex]\frac{4(1-\frac{1}{4} ^{10}) }{1-\frac{1}{4} }[/tex]
= [tex]\frac{4(1-\frac{1}{1048576}) }{\frac{3}{4} }[/tex]
= [tex]\frac{16}{3}[/tex] ( [tex]\frac{1048575}{1048576}[/tex] )
= [tex]\frac{16}{3}[/tex] × 0.9999....
= 5.33 ( to the nearest hundredth )
