SOLUTION: Use the addition problems below to answer the question. Based on this pattern, what is the sum of 1/2+1/4+1/8+1/16+...+1/1024?

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Question 854204: Use the addition problems below to answer the question.
Based on this pattern, what is the sum of
1/2+1/4+1/8+1/16+...+1/1024?
Found 2 solutions by richwmiller, aditya2117:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
1/1024= 1/2 * 1/2^(n - 1)
n=10
S=1/2*(1 - 1/2^10)/(1 - 1/2)
S=1023/1024 which is almost 1
We know that it must be more than 3/4 since just the first two terms are 1/2+1/4 which is 3/4.
The other tutor's answer
1023/4096 is less than 1/4

Answer by aditya2117(32) (Show Source):
You can put this solution on YOUR website!
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.)