用裂项法解,1/2 = 1 - 1/2,1/4 = 1/2 - 1/4,1/8 = 1/4 - 1/8,原式就等于
1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 ...+ 1/512 - 1/1024
所以=1 - 1/1024 = 1023/1024
用裂项法解,1/2 = 1 - 1/2,1/4 = 1/2 - 1/4,1/8 = 1/4 - 1/8,原式就等于
1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 ...+ 1/512 - 1/1024
所以=1 - 1/1024 = 1023/1024