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计算1024-512-...-32-16-8-4-2-1-1/2-1/4-...-1/512-1/1024=,
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1024-512-...-32-16-8-4-2-1-1/2-1/4-...-1/512-1/1024
=1024-(512+256+……+32+16+8+4+2+1+1/2+……+1/512+1/1024)
=1024-［2^9+2^8+……+2^5+2^4+2^3+2^2+2^1+1+1/2+(1/2)^2+……+(1/2)^9+(1/2)^10］
=1024-2^9*［1-(1/2)^20］/(1-1/2)
=1024-2^10*［1-(1/2)^20］
=1024-2^10+(1/2)^10
=(1/2)^10
=1/1024
=1024-(512+256+……+32+16+8+4+2+1+1/2+……+1/512+1/1024)
=1024-［2^9+2^8+……+2^5+2^4+2^3+2^2+2^1+1+1/2+(1/2)^2+……+(1/2)^9+(1/2)^10］
=1024-2^9*［1-(1/2)^20］/(1-1/2)
=1024-2^10*［1-(1/2)^20］
=1024-2^10+(1/2)^10
=(1/2)^10
=1/1024
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