Câu 1:

`-(48+125)-(350+75-48)`

`=-48-125-350-75+48`

`=-48+48-(125+75)-350`

`=0-200-350`

`=-550`

Câu 2:

Ta có: \(S=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{9^2}< \dfrac{1}{2^2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{8.9}\)

\(=\dfrac{1}{2^2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{8}-\dfrac{1}{9}\)\(=\dfrac{1}{4}+\dfrac{1}{2}-\dfrac{1}{9}=\dfrac{23}{36}< \dfrac{32}{36}=\dfrac{8}{9}\). (1)

Ta lại có: \(S=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{9^2}>\dfrac{1}{2^2}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\)

\(=\dfrac{1}{2^2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=\dfrac{1}{2^2}+\dfrac{1}{3}-\dfrac{1}{10}=\dfrac{19}{20}>\dfrac{8}{20}=\dfrac{2}{5}\). (2)

Từ (1) và (2) suy ra đpcm.

Câu 3:

c) $n+2$ là ước cửa $5n-1\Rightarrow 5n-1$ $\vdots$ $n+2$

$5(n+2)-11$ $\vdots$ $n+2$

Do $5(n+2)$ $\vdots$ $n+2\Rightarrow 11$ $\vdots$ $n+2$

$\Rightarrow n+2\in Ư(11)=\{\pm1;\pm11\}$

Ta có bảng sau:

n+2         -11          -1            1             11

n             -13           -3           -1             9

Vậy $n=\{-13;-3;-1;9\}$

Em tham khảo

$\text{a) Xét hiệu:{5n-1}-5{n+2} : n+2}$

$\text{⇔5n-1-5n-10 : n-2}$

$⇔-11 : n-2$

$⇔n-2∈Ư(11)={±1,±11}$

$\text{Ta có bảng:}$

$\text{n-2 | 1 | -1 | 11 |-11|}$

$\text{n    | 3  | 1  | 13 | -9 |}$

$\text{Vậy n={3,1,13,-9}}$

$\text{b) Ta có x÷3 dư 2}$

$⇒x-2 ÷3$

$⇒x-2∈B(3)={0,3,6,9,12,15,18,21}$

$\text{Ta có bảng:}$

$\text{x-2 |0 | 3 | 6 |  9| 12| 15 |18 |21|}$

$\text{x    | 2| 5 | 8 | 11| 15| 17|20 |23 |}$

$\text{Vì 0<x<20⇒x={2,5,8,11,15,17}}$

$\text{Xin hay nhất}$