Gọi ƯCLN(7n+4,5n+3) = d (d ∈ N)

\(\Rightarrow\) \(\begin{cases}7n+4\vdots d\\ 5n+3\vdots d\end{cases}\Rightarrow\begin{cases}5\left(7n+4\right)\vdots d\\ 7\left(5n+3\right)\vdots d\end{cases}\Rightarrow\begin{cases}35n+20\vdots d\\ 35n+21\vdots d\end{cases}\)

⇒(35n + 21 - 35n - 20\(\)) ⋮ d ⇒ 1 ⋮ d

Mà d ∈ N

⇒ d = 1

Vậy với mọi số tự nhiên thì \(\frac{7n+4}{5n+3}\) là phân số tối giản

x + 2x + 3x + ... +100x = 50500

x(1 + 2 + 3 + ... + 100) = 50500

x[(1 + 100) * 100 : 2] = 50500

x[101 * 100 : 2] = 50500

x[10100 : 2] = 50500

⇒ 5050x = 50500

x = 50500 : 5050

x = 10

Vậy x = 10

tham khảo

1. He received a letter from his penpal last week.

(-) He didn’t receive a letter from his penpal last week.
(?) Did he receive a letter from his penpal last we?

2. She taught us English last year.

(-) She didn’t teach us English last year.
(?) Did she teach you English last year?

3. They did their homework carefully.

(-) They didn’t do their homework carefully.
(?) Did they do their homework carefully?

4. The Robinsons bought a lot of souvenirs.

(-) The Robinsons didn’t buy a lot of souvenirs.
(?) Did the Robinsons buy a lot of souvenirs?

5. Tourists ate seafood at that famous restaurant.
(-) The tourists didn’t eat seafood at that famous restaurant.
(?) Did the tourists eat seafood at that famous restaurant?

Cho mình link nick bạn ấy

ở đâu vậy bạn?

Đặt \(A=\frac{25}{1\cdot6}+\frac{25}{6\cdot11}+\cdots+\frac{25}{25\cdot31}\)

\(A=5\cdot\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\cdots+\frac{5}{26\cdot31}\right)\)

\(A=5\cdot\left(\frac11-\frac16+\frac16-\frac{1}{11}+\cdots+\frac{1}{26}-\frac{1}{31}\right)\)

\(A=5\cdot\left(\frac11-\frac{1}{31}\right)\)

\(A=5\cdot\frac{30}{31}\)

\(A=\frac{150}{31}\)

Vậy \(A=\frac{150}{31}\)

C.34

[sửa]

a. 8 921 x 4 + 8 921 + 7 - 8 921

= 8 921 x (4 + 7 - 1)

= 8 921 x 10

= 89 210

b. 22 775 - 823 + 3 832 + 2 225

= (22 775 + 2 225) + (3 832 - 823)

= 25 000 + 3 009

= 28 009

a. 8 921 x 4 + 8 921 + 7 - 8 921

= 8 921 x (4 + 7 - 1)

= 8 921 x 1

= 89 210

b. 22 775 - 823 + 3 832 + 2 225

= (22 775 + 2 225) + (3 832 - 823)

= 25 000 + 3 009

= 28 009