-1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024=?
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![-1/2+1/4-1/8+1/16-1/32+1/64-.+1/1024=?](/uploads/image/z/387967-31-7.jpg?t=-1%2F2%2B1%2F4-1%2F8%2B1%2F16-1%2F32%2B1%2F64-.%2B1%2F1024%3D%3F)
-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