1/2+3/4+7/8+15/16+31/32+63/64=127/128=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 16:31:31
![1/2+3/4+7/8+15/16+31/32+63/64=127/128=?](/uploads/image/z/28847-47-7.jpg?t=1%2F2%2B3%2F4%2B7%2F8%2B15%2F16%2B31%2F32%2B63%2F64%3D127%2F128%3D%3F)
1/2+3/4+7/8+15/16+31/32+63/64=127/128=?
1/2+3/4+7/8+15/16+31/32+63/64=127/128=?
1/2+3/4+7/8+15/16+31/32+63/64=127/128=?
等于(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)
=7-(1/2+1/4+1/8+1/16+1/32+1/64+1/128)
=7-127/128
=6又1/128
等于(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)
=7-(1/2+1/4+1/8+1/16+1/32+1/64+1/128)
=7-127/128
=6又1/128
原式
=(1-1/2)+(1-1/4)+(1-1/8)+(1-1/16)+(1-1/32)+(1-1/64)+(1-1/128)
=7-(1/2+1/4+1/8+1/16+1/32+1/64+1/128)
=7-(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128)
=7-(1-1/128) (中间正负抵消了)
=7-1+1/128
=6又1/128