1/2+1/4+1/8+1/16+1/32=(1/2+1/4+1/8+1/16+1/32+1/32)-1/32=(1/2+1/4+1/8+1/16+1/16)-1/32=(1/2+1/4+1/8+1/8)-1/32=(1/2+1/4+1/4)-1/32=(1/2+1/2)-1/32=1-1/32=31/32