1/1024+1/512+1/256+``````+1/2+1+2+4+8``````+512是整数，能进行简便运算的要简便。

Question

1/1024+1/512+1/256+``````+1/2+1+2+4+8``````+512
是整数，能进行简便运算的要简便。

Answer 1

1/1024+1/512+1/256+``````+1/2+1+2+4+8``````+512
=(1/1024+1/1024+1/512+1/256+...+1/2)+(1+1+2+4+...+512)-1/1024-1
=(1/512+1/512+1/256+...+1/2)+(2+2+4+...+512)-1/1024-1
=(1/256+1/256+...+1/2)+(4+4+...+512)-1/1024-1
=(1/2+1/2)+(512+512)-1/1024-1
=1+1024-1/1024-1
=1024-1/1024
=1023又1023/1024