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222-9+11+12:2*14+14 = ? ( )

## Toán Lớp 7: Bài 6(1đ): Tìm thương biết A:B biết A=9/1+8/2+7/3+…+1/9 B=1/2+1/3+1/4+…+1/10

Toán Lớp 7: Bài 6(1đ): Tìm thương biết A:B biết
A=9/1+8/2+7/3+…+1/9
B=1/2+1/3+1/4+…+1/10

1. Giải đáp:
$\dfrac AB=10$.
Lời giải và giải thích chi tiết:
$\dfrac AB=\dfrac{\dfrac91+\dfrac82+\dfrac73\ +\,.\!.\!.+\ \dfrac19}{\dfrac12+\dfrac13+\dfrac14\ +\,.\!.\!.+\ \dfrac1{10}}\\\Rightarrow \dfrac AB=\dfrac{\!\!\bigg(\overbrace{1+1\ +\,.\!.\!.+\ 1}^{\large9}\bigg)+\dfrac82+\dfrac73\ +\,.\!.\!.+\ \dfrac19}{\dfrac12+\dfrac13+\dfrac14\ +\,.\!.\!.+\ \dfrac{1}{10}}{}\\\Rightarrow \dfrac AB=\dfrac{\left(1+\dfrac82\right)\!+\!\left(1+\dfrac73\right)+\,.\!.\!.+\left(1+\dfrac19\right)\!+1}{\dfrac12+\dfrac13+\dfrac14\ +\,.\!.\!.+\ \dfrac{1}{10}}\\\Rightarrow \dfrac AB=\dfrac{\dfrac{10}2+\dfrac{10}3\ +\,.\!.\!.+\ \dfrac{10}9+\dfrac{10}{10}}{\dfrac12+\dfrac13+\dfrac14\ +\,.\!.\!.+\ \dfrac{1}{10}}\\\Rightarrow \dfrac AB=\dfrac{10.\!\left(\dfrac12+\dfrac13+\dfrac14\ +\,.\!.\!.+\ \dfrac19+ \dfrac{1}{10}\right)}{\dfrac12+\dfrac13+\dfrac14\ +\,.\!.\!.+\ \dfrac19+\dfrac{1}{10}}\\\Rightarrow \dfrac AB=10$
Vậy $\dfrac AB=10$.

2. +)A=9/1+8/2+7/3+…+1/9
=(9-1-1-…-1)+(8/2+1)+(7/3+1)+…+(1/9+1)
=1+10/2+10/3+…+10/9
=10/2+10/3+10/4+…+10/10
=10.(1/2+1/3+1/4+…+1/10)
+)B=1/2+1/3+1/4+…+1/10
=>A/B=(10.(1/2+1/3+1/4+…+1/10))/(1/2+1/3+1/4+…+1/10)=10