What's the matter?

I have a cough/ fever (an itchy)

Tôi học nhiều lắm đặc biệt là Olm và hoc24

Đặt \(A=\frac{2}{3 \times5}+\frac{2}{5 \times7}+...+\frac{2}{203 \times2025}\)

\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\ldots+\frac{1}{2023}-\frac{1}{2025}\)

\(A=\frac{1}{3}-\frac{1}{2025}\)

\(A=\frac{675}{2025}-\frac{1}{2025}=\frac{674}{2025}\)

Vậy \(A=\frac{674}{2025}\)

Đặt \(A=\frac{2}{3\times5}+\frac{2}{5\times7}+\cdots+\frac{2}{203\times2025}\)

\(A=\frac13-\frac15+\frac15-\frac17+\cdots+\frac{1}{2023}-\frac{1}{2025}\)

\(A=\frac13-\frac{1}{2025}\)

\(A=\frac{2025}{6075}-\frac{3}{6075}=\frac{2022}{6075}\)

Vậy \(A=\frac{2022}{6075}\)

(-6,5) * 2,8 + 2,8 * (-3,5)

= 2,8 * [(-6,5) + (-3,5)]

= 2,8 * (-10)

= -28

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