1/2+1/4+1/8...1/1024
=1/2+1/4+1/8...1/1024+1/1024-1/1024
=1/2+1/4+1/8...+1/512+1/512-1/1024
=……
=1/2+1/4+1/8+1/8-1/1024
=1/2+1/4+1/4-1/1024
=1/2+1/2-1/1024
=1-1/1024
=1023/1024