Bài 3 :

c) \(\dfrac{m}{5}-\dfrac{2}{n}=\dfrac{2}{5}\)

\(\Leftrightarrow\) \(\dfrac{m}{5}-\dfrac{2}{5}=\dfrac{2}{n}\)

\(\Leftrightarrow\) \(\dfrac{m-2}{5}=\dfrac{2}{n}\)

\(\Rightarrow\) ( m - 2 ) . n = 10

10 có các ước là : \(\pm1;\pm2;\pm5;\pm10\)

*\(\left\{{}\begin{matrix}m-2=1\\n=10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=3\\n=10\end{matrix}\right.\)

*\(\left\{{}\begin{matrix}m-2=-1\\n=-10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=1\\n=-10\end{matrix}\right.\)

*\(\left\{{}\begin{matrix}m-2=10\\n=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=12\\n=1\end{matrix}\right.\)

*\(\left\{{}\begin{matrix}m-2=-10\\n=-1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=-8\\n=-1\end{matrix}\right.\)

*\(\left\{{}\begin{matrix}m-2=2\\n=5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=4\\n=5\end{matrix}\right.\)

*\(\left\{{}\begin{matrix}m-2=-2\\n=-5\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=0\\n=-5\end{matrix}\right.\)

*\(\left\{{}\begin{matrix}m-2=5\\n=2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=7\\n=2\end{matrix}\right.\)

*\(\left\{{}\begin{matrix}m-2=-5\\n=-2\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}m=-3\\n=-2\end{matrix}\right.\)

Vậy có 8 cặp (m,n) thỏa mãn : (3,10) ; (1,-10) ; (12,1) ; (-8,-1) ; (4,5) ; (0,-5) ; (7,2) ; (-3,-2) .

Gọi ước chung lớn nhất của 12n+1 và 30n+ 2 là d

\(\Rightarrow\) ( 12n+1) \(⋮\) d và ( 30n+2 ) \(⋮\) d

\(\Rightarrow\) \(\left[5\left(12n+1\right)-2\left(30n+2\right)\right]⋮d\)

\(\Leftrightarrow\) ( 60n + 5 - 60n - 4 ) \(⋮d\)

\(\Leftrightarrow\) 1 \(⋮\) d hay d= 1

Vậy ước chung lớn nhất của 12n+ 1 và 30n+2 là 1 hay \(\dfrac{12n+1}{30n+2}\) là phân số tối giản .

1) Are there four pictures on the wall ?

2) Which school does she go to ?

3) Is there any milk in the can ?

4) How many brothers and sisters does he have ?

5) What does your mother like ?

6) Where does he work ?

7) How many bookstore are there near your house ?

8) When do you have it ?

9) What is her school ?

10) How often do you walk to school ?

Nếu đk thì mik sẽ đi vòng quanh thế giới , khám phá vũ trụ .

b) Đặt A vào biểu thức, ta có :

A= 1+ 2 + 2² + 2³ + 2⁴ +...+ 2⁹⁹ + 2¹⁰⁰

2A= 2 + 2² +2³ + 2⁴ + 2⁵ +...+ 2¹⁰⁰ + 2²⁰¹

2A - A= 2²⁰¹ - 1

a) \(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)

= \(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

= \(1-\dfrac{1}{101}\)

= \(\dfrac{100}{101}\)

b) \(\dfrac{5}{1.3}+\dfrac{5}{3.5}+\dfrac{5}{5.7}+...+\dfrac{5}{99.101}\)

= \(\dfrac{1}{3}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

= \(\dfrac{1}{3}\left(1-\dfrac{1}{101}\right)\)

= \(\dfrac{1}{3}.\dfrac{100}{101}\)

= \(\dfrac{100}{303}\)