初一数学题(写过程)

设S=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256，
则S/2= 1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512,
两式相减得(对齐相减）：
S/2=1/2-1/512=255/512,
所以S=255/256.

1/2+1/4=3/4=1-1/4
1/2+1/4+1/8=7/8=1-1/8
1/2+1/4+1/8+1/16=15/16=1-1/16

.....
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=1-1/256
=255/256

设S=1/2+1/4+...+1/256 (1) 所以 2S=1+1/2+1/4+...+1/128 (2)
用(2)-(1)得 S=1-1/256=255/256