-1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024=?

-1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024=?
-1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024=?

-1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024=?
设原式= A
则：
A= -1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024
2A= -1+1/2-1/4+1/8-1/16+1/32-1/64+.+1/512
两式相加,中间各项正负相消,得：
3A= -1+1/1024= -1023/1024
所以：
A= -341/1024
即：
-1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024= -341/1024

设A=-1/2+1/4-1/8+1/16-1/32+1/64-......+1/1024
1/2A=-1/4+1/8-1/16+1/32-1/64+1/128-。。。。。+1/2048
A+1/2A=-1/2+1/2048=-1023/2048
3/2A=-1023/2048
A=-341/1024
即原式=-341/1024

原式=-512/1024+256/1024-128/1024+64/1024-32/1024+16/1024-8/1024+4/1024-2/1024+1/1024=（-256-64-16-4-1）/1024=-341/1024