简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127+218
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 18:28:36
![简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127+218](/uploads/image/z/604704-48-4.jpg?t=%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%3A1%2F2%2B3%2F4%2B7%2F8%2B15%2F16%2B31%2F32%2B63%2F64%2B127%2B218)
简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127+218
简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127+218
简便计算:1/2+3/4+7/8+15/16+31/32+63/64+127+218
最后一项应该是"127/128"..
然后原式=(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)=7-1/2[1-(1/2)^7]/(1-1/2)=769/128.
每一项都等于1减去2的次方分之一.