1/2+1/4+1/8+1/16+1/32+…+1/1024=?1/2+1/4+1/8+1/16+1/32+…+1/1024=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/25 03:40:33
1/2+1/4+1/8+1/16+1/32+…+1/1024=?1/2+1/4+1/8+1/16+1/32+…+1/1024=?1/2+1/4+1/8+1/16+1/32+…+1/1024=?1/2+

1/2+1/4+1/8+1/16+1/32+…+1/1024=?1/2+1/4+1/8+1/16+1/32+…+1/1024=?
1/2+1/4+1/8+1/16+1/32+…+1/1024=?
1/2+1/4+1/8+1/16+1/32+…+1/1024=?

1/2+1/4+1/8+1/16+1/32+…+1/1024=?1/2+1/4+1/8+1/16+1/32+…+1/1024=?
1/2+1/4=1-1/4=3/4
1/2+1/4+1/8=1-1/8=7/8
类推
1/2+1/4+1/8+1/16+1/32+…+1/1024=1-1/1024=1023/1024

1/2+1/4+1/8+...+1/1024
=512/1024+256/1024+128/1024+...+1/1024
=(512+256+128+64+32+16+8+4+2+1)/1024
=(2^9+2^8+2^7+2^6+2^5+2^4+2^3+2^2+2^1+2^0)/1024(此后为等比数列求和)
=(1*2^(1-1)+1*2^(2-1)+1*2^(3-1)+...+1*2^(10-1))/1024
=1*(1-2^10)/(1-2)/1024
=1*(1-1024)/-1/1024
=1023/1024

^ 符号是次方的意思。比如2^ 3就是二的三次方。

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