Question

1+2+4+8+16+32+64+128+256+512=

Answer 1

=1024-1=1023

Answer 2

=1111111111 base 2
=1023 base10
=3FF base 12

Answer 3

This is actually a geometric profession,with the common ratio 2 the sum of a geometric progression is give by \[\frac{a(r^n-1)}{(r-1)}\],where n = number of terms,a =first term and r is the common ratio.

Here a = 1,n=10,so the sum is :

\[\frac{1(2^{10}-1)}{2-1}=2^{10}-1=1023\]