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