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

问题描述:

-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