作业帮和式(2+1/2)+(4+1/4)+(8+1/8)+...+(1024+1/1024)=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/10 18:41:45
和式(2+1/2)+(4+1/4)+(8+1/8)+...+(1024+1/1024)=?
和式(2+1/2)+(4+1/4)+(8+1/8)+...+(1024+1/1024)=?
和式(2+1/2)+(4+1/4)+(8+1/8)+...+(1024+1/1024)=?
(2+1/2)+(4+1/4)+(8+1/8)+...+(1024+1/1024)
=(2+4+8+……+1024)+(1/2+1/4+1/8+……+1/1024)
令T=2+4+8+……+1024
=2+2^2+2^3+……+2^10
=2(1-2^10)/(1-2)
=2(2^10-1)
=2(1024-1)
=2*1023
=2046
令S=1/2+1/4+1/8+……+1/1024
则2S=1+1/2+1/4+……+1/512
S=2S-S=1-1/1024=1023/1024
原式=2046+1023/1024=2046又1023/1024
(2+1/2)+(4+1/4)+(8+1/8)+...+(1024+1/1024)
=（2+4+8+……+1024）+（1/2+1/4+1/8+……+1/1024）
=1024×2-2+（1-1/1024）
=2048-2+1023/1024
=2046又1023/1024