1-1/2+1/4-1/8+1/16-1/32+1/64-1/128+1/256-1/512+1/1024-1/2048

1-1/2+1/4-1/8+1/16-1/32+1/64-1/128+1/256-1/512+1/1024-1/2048
1-1/2+1/4-1/8+1/16-1/32+1/64-1/128+1/256-1/512+1/1024-1/2048

1-1/2+1/4-1/8+1/16-1/32+1/64-1/128+1/256-1/512+1/1024-1/2048
1-1/2+1/4-1/8+1/16-1/32+1/64-1/128+1/256-1/512+1/1024-1/2048=1-(-1/2)^12/(1+1/2)
=2/3[1-(1/2)^12]
=(2/3)*(4095)4096
=4095/3*2048
=1365/2048