Question 854204
in the sequence , 1st Term = 1/2 , C.R.(Common Ratio) = (1/4)/(1/2)=1/2
let the no. of terms be n,
Accordingly,
1/2 * (1/2)^(n-1) = 1/1024 [The first term is multiplied by 1/2 constantly to get
                            1/1024 (n-1) times]
=> (1/2)^[1+(n-1)]= 2^(-10)
=>  2^-(n) = 2^ (-10)
=>  n =10   
No. of terms = 10 
Now, Sum of first n terms of a G.P. series = a(r^n - 1)/(r-1) where r#1
                                             [a=1st term, r=C.R,n = no.of terms] 
                                           = 1/2[ (1/2)10 - 1 ]/(1/2 - 1)
                                           = 1/2 (1/1024 - 1)* (-1/2)  
                                           = -1/4 * -1023/1024
                                           = -1 * -1023 / 4*1024
                                           = 1023/4096 (Ans.)