a, 350 ml = \(\dfrac{350}{1000}\)l = \(\dfrac{7}{20}\) l

b, 600 ml = \(\dfrac{600}{1000}\) l = \(\dfrac{3}{5}\) l

c, 2020ml = \(\dfrac{2020}{1000}\) l = \(\dfrac{101}{50}\) l 

100 kg = \(\dfrac{100}{100}\) tạ = \(\dfrac{1}{1}\) tạ 

100kg = \(\dfrac{100}{1000}\) tấn = \(\dfrac{1}{10}\) tấn

2020 kg = \(\dfrac{2020}{100}\) tạ = \(\dfrac{101}{5}\) tạ 

2020 kg = \(\dfrac{2020}{1000}\) tấn = \(\dfrac{101}{5}\) tấn

35kg = \(\dfrac{35}{100}\) tạ = \(\dfrac{7}{20}\) tạ

35kg = \(\dfrac{35}{1000}\) tấn = \(\dfrac{7}{200}\) tấn

500 g = \(\dfrac{500}{100000}\) tạ = \(\dfrac{1}{200}\) tạ 

500 g =\(\dfrac{500}{1000000}\)tấn =\(\dfrac{1}{2000}\) tấn 

2020 kg  = \(\dfrac{101}{50}\) tấn nhé lúc nãy mình thiếu số 0

(7x - 11)³ = 2⁵.5² + 200

<=> (7x - 11)³  = 32.25 + 200

<=> (7x - 11)³ = 800 + 200

<=> (7x - 11)³ = 1000

<=> (7x - 11)³ = 10³

<=> 7x - 11 = 10

<=> 7x = 21

<=> x = 3 

Điều kiện: x > 0

Khoảng cách giữa hai số là 4

Dãy số trên có số số hạng: 

\(\dfrac{x-1}{4}+1\)

Tổng của dãy số trên:

\(\dfrac{\left(x+1\right)\left(\dfrac{x-1}{4}+1\right)}{2}=4950\) (*)

(*) \(\Leftrightarrow\left(x+1\right)\left(\dfrac{x-1}{4}+1\right)=9900\)

\(\Leftrightarrow\dfrac{\left(x+1\right)\left(x+3\right)}{4}=9900\)

\(\Leftrightarrow\left(x+1\right)\left(x+3\right)=39600\)

\(\Leftrightarrow x^2+4x+3=39600\)

\(\Leftrightarrow x^2+4x-39597=0\)

\(\Leftrightarrow x^2+2x+2x+4-39601=0\)

\(\Leftrightarrow\left(x+2\right)^2=39601\)

\(\Leftrightarrow\left(x+2\right)^2=199^2\)

\(\Leftrightarrow\left[{}\begin{matrix}x+2=199\\x+2=-199\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=197\\x=-201\left(loại\right)\end{matrix}\right.\)

Vậy x = 197.

\(2+4+6+8+...+2x=210\)

\(\Rightarrow1+2+3+4+...+x=105\)

\(\Rightarrow\dfrac{x.\left(1+x\right)}{2}=105\)

\(\Rightarrow x.\left(1+x\right)=210\)

\(\Rightarrow x=14\)

Vậy x = 14.

\(x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+30\right)=1240\)

\(\Rightarrow31x+\left(1+2+3+...+30\right)=1240\)

\(\Rightarrow31x+\dfrac{\left(30+1\right)\left[\left(30-1\right):1+1\right]}{2}=1240\)

\(\Rightarrow31x+465=1240\)

\(\Rightarrow31x=775\)

\(\Rightarrow x=25\)

Vậy x = 25.

Tránh các giá trị x, ta lập dãy số:

1; 2; 3;...;30

Có 30 số hạng, tổng của dãy trên là: (1 + 30) x 30 : 2 = 465

Ta đặt lại biểu thức như sau:

X x 31 + 465 = 1240

X x 31           = 1240 - 465

X x 31           = 775

X                   = 775 : 31 = 25

Đặt \(S=\)\(\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{20}}\)
\(\Rightarrow9S=1+\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{18}}\)
\(\Rightarrow9S-S=\left(1+\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{18}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{20}}\right)\)
\(\Rightarrow8S=1-\dfrac{1}{3^{20}}\)
\(\Rightarrow S=\dfrac{1-\dfrac{1}{3^{20}}}{8}\)

\(A=\dfrac{9}{1.2}+\dfrac{9}{2.3}+\dfrac{9}{3.4}+...+\dfrac{9}{98.99}+\dfrac{9}{99.100}\)
\(=9\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{98.99}+\dfrac{1}{99.100}\right)\)
\(=9\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{98}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\right)\)
\(=9\left(1-\dfrac{1}{100}\right)\)
\(=9.\dfrac{99}{100}\)
\(=\dfrac{891}{100}\)

\(A=\dfrac{9}{1.2}+\dfrac{9}{2.3}+\dfrac{9}{3.4}+...+\dfrac{9}{98.99}+\dfrac{9}{99.100}\)

\(=9.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{98.99}+\dfrac{1}{99.100}\right)\)

\(=9.\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\)

\(=9.\left(1-\dfrac{1}{100}\right)\)

\(=9.\dfrac{99}{100}\)

\(=\dfrac{891}{100}\).

\(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{30}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{29}{30}\)

\(=\dfrac{1.2.3...29}{2.3.4...30}\)

\(=\dfrac{1}{30}\)

\(B=1\dfrac{1}{3}.1\dfrac{1}{8}.1\dfrac{1}{15}.1\dfrac{1}{24}...1\dfrac{1}{168}\)

\(=\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.\dfrac{25}{24}...\dfrac{169}{168}\)

\(=\dfrac{4.9.16.25...169}{3.8.15.24...168}\)

\(=\dfrac{2.3.4...13}{1.2.3...12}.\dfrac{2.3.4...13}{3.4.5...14}\)

\(=13.\dfrac{1}{7}\)

\(=\dfrac{13}{7}\).

A = \(\dfrac{1}{2}x\dfrac{2}{3}x\dfrac{3}{4}x...x\dfrac{29}{30}=1x1x1x...x\dfrac{1}{30}=\dfrac{1}{30}\)

B = \(\dfrac{4}{3}x\dfrac{9}{8}x\dfrac{16}{15}x\dfrac{25}{24}x...x\dfrac{169}{168}=1x1x1x1x...x\dfrac{13}{7}=\dfrac{13}{7}\)

Câu B em chưa rõ cách làm nhanh cho lắm. Nếu ko cần tính nhanh thì chị có thể giải bình thường ra giấy ha.