a)7^x-3.7²³=4.7²³

7^x           =4.7²³+3.7²³

7^x           =7²³.(4+3)

7^x           =7²³.7

7^x           = 7²⁴

=> x = 24

b)2.5^x+1+3.5²¹=5²²

2.5^x+1            = 5²²-3.5²¹

2.5^x+1            = 5²¹(5-3)

2.5^x+1            =5²¹.2

=>5^x+1 = 5²¹

=>x+1 = 21

 x       = 21 - 1

 x       = 20

a. 7\(^x\)- 3.27^23 = 4.7^23

7^x = 7.7^23

7^x = 7^24

x = 24

b. 

\(A=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{2021\cdot2023}\)

\(A=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\)

\(A=\dfrac{1}{1}-\dfrac{1}{2023}\\ A=\dfrac{2023}{2023}-\dfrac{1}{2023}\\ A=\dfrac{2022}{2023}\)

$A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}$

$A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}$

$A=\frac{1}{1}-\frac{1}{99}$

$A=\frac{98}{99}$

=

21​−5

Ta có: \(A=\frac{9}{2\cdot5}-\frac{11}{3\cdot5}+\frac{13}{3\cdot7}-\frac{15}{4\cdot7}+\cdots+\frac{197}{49\cdot99}-\frac{199}{50\cdot99}\)

\(=2\left(\frac{9}{4\cdot5}-\frac{11}{5\cdot6}+\frac{13}{6\cdot7}-\frac{15}{7\cdot8}+\cdots+\frac{197}{98\cdot99}-\frac{199}{99\cdot100}\right)\)

\(=2\left(\frac14+\frac15-\frac15-\frac16+\frac16+\frac17-\cdots+\frac{1}{98}+\frac{1}{99}-\frac{1}{99}-\frac{1}{100}\right)\)

\(=2\left(\frac14-\frac{1}{100}\right)=2\cdot\frac{24}{100}=\frac{48}{100}=\frac{12}{25}\)

Câu 2:

\(D=\dfrac{3}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(=\dfrac{3}{2}\cdot\dfrac{100}{101}=\dfrac{150}{101}\)

Câu 3: 

\(E=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{205}-\dfrac{1}{207}\right)\)

\(=2\cdot\left(1-\dfrac{1}{207}\right)=2\cdot\dfrac{206}{207}=\dfrac{412}{207}\)

Câu 5: 

\(G=\dfrac{1}{4}\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}\right)\)

\(=\dfrac{1}{4}\cdot\dfrac{16}{17}=\dfrac{4}{17}\)

3 . 6 = 3 . 4 + 2 . 3 rùi đấy bạn, bn xét từng tích rùi sẽ thấy thôi.

Sorano Yuuki !!! Mình hiểu rồi . Thì ra người ta tách sai =.= Cảm ơn nhé .

Đáng nhẽ là . Ta thấy 1.4=1.(2+2)

2.5 = 2.(2 + 3)
3.6 = 3.(2 + 4)
4.7 = 4.(2 + 5)
……

n(n + 3) = n(n + 1) + 2

mình sẽ ủng hộ bạn có câu trả lời đúng nhất nhé