简算,在线等

设A=1+3/2+5/4+7/8+9/16+11/32+13/64

2A=2+3+5/2+7/4+9/8+11/16+13/32

2A-A=4+2/2+2/4+2/8+2/16+2/32

A=4+1+1/2+1/4+1/8+1/16=5+1/2+1/4+1/8+1/16+1/16-1/16

=5+1/2+1/4+1/8+1/8-1/16

=5+1/2+1/4+1/4-1/16

=5+1/2+1/2-1/16

=6-1/16

=95/16

S=1+3/2+5/4+7/8+9/16+11/32+13/64
S/2=1/2+3/4+5/8+7/16+9/32+11/64+13/128
两个式子相减
S/2=1+1+1/2+1/4+1/8+1/16+1/32-13/128
=2+111/128
=2又111/128

1+3/2+5/4+7/8+9/16+11/32+13/64
=（64+3*32+5*16+7*8+9*4+11*2+13）/64
=367/64

设M=1+3/2+5/4+7/8+9/16+11/32+13/64
N=1/2M=1/2+3/4+5/8+7/16+9/32+11/64+13/128
M-N=1+1+1/2+1/4+1/8+1/16+1/32-13/128=1/2M

3+32/64+16/64+56/64+36/64+22/64+13/64

通分.3+(32+16+56+36+44+13)/64=6+5/64