Verified answer

2047

It's binary dude, 2^n - 1. In this case n = 11.

1+2+4+...+1024

= 1 + (1*2) + (2*2) + ........ 1024

first term, a = 1

common ratio, r = 2

nth term, an = ar^(n-1)

since nth term, an = 1024

ar^(n-1) = 1024

1* (2)^(n-1) = 1024

2^(n-1) = 1024

2^n / 2 = 1024

2^n = 2048

Sum of n terms, Sn = a (r^n - 1) / (r - 1)

Sn = 1 [ 2^n - 1 ] / (2 - 1)

= (2048 - 1)

= 2047

2044

0^2 + 1^2 + ... + 10^2 = 2044