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avatar+312 

What is the sum of \(1+2+4+8+16+ \cdots + 1024\)?

 Jan 5, 2021
 #1
avatar+312 
+1

This is a finite geometric series with first term 1, common ratio 2 and 11 terms. Thus the sum is:

\(frac{1(1-2^{11})}{1-2} = \frac{1-2^{11}}{-1} = 2^{11}-1 = 2048-1 = \boxed{2047}\).

 Jan 5, 2021
 #2
avatar+114094 
+2

Note  that   we  can write

 

Sum  =   (last term) * 2   -  1

 

So

 

Sum  = 2(1024)   - 1   =  2047

 

 

cool cool cool

 Jan 5, 2021
 #3
avatar+312 
0

I did think about it that way but that is right

 Jan 5, 2021

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