S=1/2+1/4+1/8+1/16+1/32+1/64
S=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64
S=1-1/64
S=63/64
S = 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64
2S = 1/2 x 2 +1/4 x 2 + 1/8 x 2 + 1/16 x 2 + 1/32 x 2 + 1/64 x 2
2S =1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32
2S - S = ( 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 ) - ( 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 )
S = 1 - 1/64
S = 63/64