A

Thx bro

Last weekend, I did something good for my family that made me feel very happy. On Saturday morning, I saw that my mother was very busy with housework. She had to cook, clean, and do the laundry. I decided to help her by cleaning the floor and washing the dishes. At first, I felt a little tired, but when I saw my mother smiling, I knew it was worth it. Later, my father praised me and said I was becoming more responsible. My younger brother also joined me, and together we finished the work quickly. That day, I learned that even small actions can bring joy to the people we love. Helping my family not only made them happy but also made me proud of myself. I will try to do more good deeds like this in the future.

Hi everyone, my name is Phuong Thao. I will introduce my family to you. Our family has 4 people including my father, my mother, my brother and me. My father is an engineer at a construction site near my home. My father is very busy. He usually had to stand outside all day. So he has a tanned skin. However, one day he still spends time playing with me. My mother is a good housewife. Every day I can eat delicious dishes that I cook. Mother takes care of her family very well. Before I go to bed, my mother usually reads me a story. My brother is 12 years old. I often play with him in my free time so my mom can do other things. I love my family very much.

sửa đề câu a  và câu b  nhá  , mik nghĩ đề như này :

  \(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)

 \(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)

= \(\frac{1}{1}-\frac{1}{215}\)

\(=\frac{214}{215}\)

b, đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{213\cdot215}\)

    \(A\cdot2=\frac{2}{1\cdot3}+\frac{2}{3.5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)

\(A\cdot2=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)

\(A\cdot2=\frac{1}{1}-\frac{1}{215}\)

\(A\cdot2=\frac{214}{215}\)

\(A=\frac{214}{215}:2\)

\(A=\frac{107}{215}\)

@ミ★Ŧɦươйǥ★彡 cảm ơn bạn nhiều

a) Áp dụng t/x dtsbn:

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{-5}=\dfrac{3x}{6}=\dfrac{2z}{-10}=\dfrac{3x-2z}{6+10}=\dfrac{48}{16}=3\)

\(\Rightarrow\left\{{}\begin{matrix}x=3.2=6\\y=3.3=9\\z=3.\left(-5\right)=-15\end{matrix}\right.\)

b) \(\dfrac{x}{10}=\dfrac{y}{-13}=\dfrac{z}{17}=\dfrac{2y}{-26}=\dfrac{3z}{51}=\dfrac{2y-3z}{-26-51}=\dfrac{77}{-77}=-1\)

\(\Rightarrow\left\{{}\begin{matrix}x=10.\left(-1\right)=-10\\y=\left(-13\right).\left(-1\right)=13\\z=17.\left(-1\right)=-17\end{matrix}\right.\)

a) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{-5}\Rightarrow\dfrac{3x}{6}=\dfrac{y}{3}=\dfrac{2z}{-10}\)

Áp dụng t/c của DTSBN, ta có: \(\dfrac{3x-2z}{6-\left(-10\right)}=\dfrac{48}{16}=3\)

\(\dfrac{x}{2}=3\Rightarrow x=6\)

\(\dfrac{y}{3}=3\Rightarrow y=9\)

\(\dfrac{z}{-5}=3\Rightarrow z=-15\)

A = (3x - 5)(2x + 11) - (2x + 3)(3x + 7)

A = 3x(2x + 11) - 5(2x+  11) - 2x(3x + 7) - 3(3x + 7)

A=  6x² + 33x - 10x - 55 - 6x² - 14x - 9x - 21

A = (6x² - 6x²) + (33x - 10x - 14x - 9x) + (-55 - 21) = -76 => không phụ thuộc vào biến x (đpcm)

B = (2x + 3)(4x² - 6x + 9) - 2(4x³ - 1)

= 2x(4x² - 6x + 9) + 3(4x² - 6x + 9) - 8x³ + 2

= 8x³ - 12x² + 18x + 12x² - 18x - 27 - 8x³ + 2

= (8x³ - 8x³) + (-12x² + 12x²) + (18x - 18x) + (-27 + 2) = -25 => không phụ thuộc vào biến x (đpcm)

A= ( 3x - 5 ) ( 2x+11) - (2x+3)(3x+7) 

=\(6x^2+23x-55-\left(6x^2+23x+21\right)\) 

=\(6x^2+23x-55-6x^2-23x-21\)  

= -76 

Vậy A không phụ thuộc vào x

B=2/3x5 + 2/5x7 + 2/7x9 + ...+2/99x101

B= 1/3 - 1/5 + 1/5 - 1/7 + 1/7 -1/9 + ... + 1/99 - 1/101

B= 1/3 - 1/101

B=98/303

( k mk nhé ! Cách làm câu a và b của mk đều đúng 100% đấy ! Dạng này mk học từ lâu rồi ! )

a, A = 1/2x3+ 1/ 3x4 + 1/4x5 + 1/5x6 + ... + 1/99x100

    A= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 -1/5 + 1/5 - 1/6 + ... + 1/99 -1/100

    A= 1/2 -1/100

    A= 49 / 100