Tính `:` `C=(1/(1.10)+1/(2.9)+1/(3.8)+...+1/(10.1))/(1+1/2+1/3+...+1/10)`
2 câu trả lời
Đáp án + Giải thích các bước giải:
Đặt `A=1+1/2+1/3+...+1/10`
`=>A=(1+1/10)+(1/2+1/9)+(1/3+1/8)+...+(1/5+1/6)`
`=>A=(10+1)/(10.1)+(9+2)/(9.2)+(8+3)/(3.8)+...+(6+5)/(5.6)`
`=>A=11/(10.1)+11/(9.2)+11/(3.8)+11/(5.6)`
`=>A=11.(1/10.1+1/9.2+1/3.8+...+1/5.6)`
Đặt `B=1/1.10+1/2.9+1/3.8+...+1/10.1`
`=>B=2/1.10+2/2.9+2/3.8+...+2/5.6`
`=>B=2.(1/1.10+1/2.9+1/3.8+...+1/5.6)`
Ta có: `C=B/A=(2.(1/1.10+1/2.9+1/3.8+...+1/5.6))/(11.(1/10.1+1/9.2+1/3.8+...+1/5.6))=2/11`
Vậy `C=2/11`
Đáp án:
`C=2/11`
Giải thích các bước giải:
`C=(1/(1.10)+1/(2.9)+1/(3.8)+...+1/(10.1))/(1+1/2+1/3+...+1/10)`
Đặt `A=1+1/2+1/3+...+1/10`
`=>A=(1+1/10)+(1/2+1/9)+(1/3+1/8)+...+(1/5+1/6)`
`=>A=(10+1)/(10.1)+(9+2)/(9.2)+(8+3)/(3.8)+...+(6+5)/(5.6)`
`=>A=11/(10.1)+11/(9.2)+11/(3.8)+11/(5.6)`
`=>A=11.(1/10.1+1/9.2+1/3.8+...+1/5.6)`
Đặt `B=1/1.10+1/2.9+1/3.8+...+1/10.1`
`=>B=2/1.10+2/2.9+2/3.8+...+2/5.6`
`=>B=2.(1/1.10+1/2.9+1/3.8+...+1/5.6)`
Vậy ta có:
`C=B/A=(2.(1/1.10+1/2.9+1/3.8+...+1/5.6))/(11.(1/10.1+1/9.2+1/3.8+...+1/5.6))=2/11`
Vậy `C=2/11`
Câu hỏi trong lớp
Xem thêm
