Answer:
The value x is 10240.
Step-by-step explanation:
The sum of the series 5(1/2)^i is x/1024.
The sum of an infinite series [tex]a_n=ar^n[/tex] is
[tex]Sum=\frac{a}{1-r}[/tex]
The given series is
[tex]a_i=5(\frac{1}{2})^i[/tex]
Here, [tex]a=5,r=\frac{1}{2}[/tex].
The sum of given series is
[tex]Sum=\frac{5}{1-\frac{1}{2}}[/tex]
[tex]\frac{x}{1024}=\frac{5}{\frac{1}{2}}[/tex]
[tex]\frac{x}{1024}=10[/tex]
[tex]x=10240[/tex]
Therefore value x is 10240.
