(y+1/2)+(y+1/4)+(y+1/8)+(y+1/16)+...+(y+1/1024)=1
2 câu trả lời
`(y+1/2)+(y+1/4)+(y+1/8)+(y+1/16)+....+(y+1/1024)=1`
`=>` $\underbrace{y+y+y+...+y}_{\text{512 số y}}$ `+(1/2+1/4+1/8+....+1/1024)=1`
Đặt `A=1/2+1/4+1/8+....+1/1024`
`=>2A=1+1/2+1/4+....+1/1012`
`=>2A-A=1-1/1024`
`=>A=1023/1024`
`=>512y+1023/1024=1`
`=>512y=1/2024`
`=>y=1/524288`
Đáp án:
`1/524288.`
Giải thích các bước giải:
Số số hạng `y: (1024-2):2+1=512` (số)
`(y+1/2)+(y+1/4)+(y+1/8)+...+(y+1/1024)=1`
`<=>512y+(1/2+1/4...+1/1024)=1`
`<=>512y+A=1(*)`
`A=1/2+1/4...+1/1024`
`2A=1+1/2...+1/512`
`A=2A-A=1-1/1024=1023/1024`
`(*)<=>512y+1023/1024=1`
`<=>512y=1/1024`
`<=>y=1/524288.`