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1/2+1/4+1/8+1/16+1/64+1/128+1/256+1/512=多少

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/23 02:55:45
1/2+1/4+1/8+1/16+1/64+1/128+1/256+1/512=多少
我急
令T=1/2+1/4+1/8+1/16+1/64+1/128+1/256+1/512
则2T=1+1/2+1/4+1/8+1/16+1/64+1/128+1/256
T=2T-T
=(1+1/2+1/4+1/8+1/16+1/64+1/128+1/256)-(1/2+1/4+1/8+1/16+1/64+1/128+1/256+1/512)
=1+1/2+1/4+1/8+1/16+1/64+1/128+1/256-1/2-1/4-1/8-1/16-1/64-1/128-1/256-1/512
=1-1/512
=511/512