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1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/14 17:21:40
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
令m=1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
两边同时乘2,得:
2m=1+1/2+1/4+1/8+...+1/128
两式相减,得:
m=1-1/256=255/256
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=(1-1/2)+(1/2-1/4)+(1/4-1/8)+...+(1/128-1/256)
=1-1/2+1/2-1/4+1/4-1/8+...+1/128-1/256
=1-1/256
=255/256