1/2-(1/2-1/4)-(1/4-1/8)-……-(1/512-1/1024)

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1/2-(1/2-1/4)-(1/4-1/8)-……-(1/512-1/1024)
1/2-(1/2-1/4)-(1/4-1/8)-……-(1/512-1/1024)

1/2-(1/2-1/4)-(1/4-1/8)-……-(1/512-1/1024)
=1/2-1/2+1/4-1/4+1/8……-1/512+1/1024
=1/1024
裂项相消,