算给你看看吧
2/8 + 3/8 + 7/16 + 15/32 + 31/64 + 63/128 + 127/256 + 255/512 + 511/1024
= (4-2)/8 + (4-1)/8 + (8-1)/16 + (16-1)/32 + (32-1)/64 + (64-1)/128
+ (128-1)/256 + (256-1)/512 + (512-1)/1024
= (1/2 - 1/4) + (1/2 - 1/8) + (1/2 - 1/16) + (1/2 - 1/32) + (1/2 - 1/64) + (1/2 - 1/128)
+ (1/2 - 1/256) + (1/2 - 1/512) + (1/2 - 1/1024)
= 9X(1/2) - (1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024)
= 9/2 - (256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1)/1024
= 9/2 - (512 - 1)/1024
= 9/2 - 1/2 + 1/1024
= 8/2 + 1/1024
= 4+ 1/1024