What is the sum of \(1+2+4+8+16+ \cdots + 1024\)?
This is a finite geometric series with first term 1, common ratio 2 and 11 terms. Thus the sum is:
\(frac{1(1-2^{11})}{1-2} = \frac{1-2^{11}}{-1} = 2^{11}-1 = 2048-1 = \boxed{2047}\).
Note that we can write
Sum = (last term) * 2 - 1
So
Sum = 2(1024) - 1 = 2047
I did think about it that way but that is right
+285 
