1. {N;H;A;T;R;G}

2. {T;o;a;n;H;c}

3. {2;9;0;7}

4. {2;3;0;4;6}

ko hiểu 

a) \(\left(6-\frac{2}{3}+\frac{1}{2}\right)-\left(5+\frac{5}{3}-\frac{3}{2}\right)-\left(3-\frac{7}{3}+\frac{5}{2}\right)\)

\(=6-\frac{2}{3}+\frac{1}{2}-5-\frac{5}{3}+\frac{3}{2}-3+\frac{7}{3}-\frac{5}{2}\)

\(=\left(-\frac{2}{3}-\frac{5}{3}+\frac{7}{3}\right)+\left(\frac{1}{2}+\frac{3}{2}-\frac{5}{2}\right)+\left(6-5-3\right)\)

\(=0+2-\frac{5}{2}+\left(-2\right)=\left(2-2\right)-\frac{5}{2}=0-\frac{5}{2}=-\frac{5}{2}\)

Câu 1:
Giả sử \(\frac{3}{5}< \frac{3+m}{5+m}\)
=) \(3.\left(5+m\right)< 5.\left(3+m\right)\)
=) \(15+3m< 15+5m\) ( Đúng vì \(15=15\)và \(3m< 5m\)) =) Điều giả sử đúng
=) \(\frac{3}{5}< \frac{3+m}{5+m}\)
* Từ điều trên ta suy ra : Nếu \(\frac{a}{b}< 1\)=) \(\frac{a}{b}< \frac{a+m}{b+m}\)
Và nếu \(\frac{a}{b}>1\)=) \(\frac{a}{b}>\frac{a+m}{b+m}\)
Câu 2 :
= \(5.\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right)\)
= \(5.\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)
= \(5.\left(\frac{1}{1}-\frac{1}{31}\right)\)= \(5.\frac{30}{31}=\frac{150}{31}\)

=> Với mọi số tự nhiên m ( như m\(\ne\)0 ) thì \(\frac{3}{5}< \frac{3+m}{5+m}\)

\(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}\)

\(=5\left(\frac{1}{1.6}+\frac{1}{6.11}+...+\frac{1}{26.31}\right)\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

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

\(=5.\frac{30}{31}\)

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

\(11\cdot\left(x-6\right)=4x+11\)

\(11x-66=4x+11\)

\(11x-4x=11+66\)

\(7x=77\)

\(\Rightarrow x=11\)

\(11.\left(x-6\right)=4x+11\)
=) \(11x-66=4x+11\)
=) \(11x-4x=11+66\)
=) \(7x=77\)
=) \(x=77:7=11\)

Ta có:

 B=1+1/2*(1+2)+1/3*(1+2+3)+..+1/20*(1+2+3+...+20)

B=1+3/2+6/3+10/4+...+210/20

=2/2+3/2+4/2+5/2+...+21/2=115

115 nhé bạn

\(50-\left[\left(50-2^3\cdot5\right)\div2+3\right]=50-\left[10\left(5-2^2\right)\div2+3\right]=50-\left(5\cdot1+3\right)=50-8=42\)

=37 nha bn

\(=100-\left[60:\left[5^2-15\right]\right]=100-\left[60:\left[25-15\right]\right]\)

\(=100-\left[60:10\right]=100-6=94\)

\(=100-\left[60:\left(5.5-3.5\right)\right]\)

\(=100-\left\{60:\left[5.\left(5-3\right)\right]\right\}\)

\(=100-\left[60:\left(5.2\right)\right]\)

\(=100-\left(60:10\right)\)

\(=100-6=104\)

Chúc cậu thành công :D

\(50-\left[\left[20-2^3\right]:2+34\right]=50-\left[\left[20-8\right]:2+34\right]\)

\(=50-\left[12:2+34\right]=50-\left[6+34\right]=50-40=10\)

=10 nha bn

\(\frac{15}{21}+\frac{4}{42}=\frac{30}{42}+\frac{4}{42}=\frac{30+4}{42}=\frac{34}{42}=\frac{17}{21}\)

\(\frac{75}{100}-\frac{2}{4}=\frac{75}{100}-\frac{50}{100}=\frac{75-50}{100}=\frac{25}{100}=\frac{1}{4}\)

\(\frac{15}{21}+\frac{4}{42}=\frac{15+2}{21}=\frac{17}{21}\)

\(\frac{75}{100}-\frac{2}{4}=\frac{15-10}{20}=\frac{5}{20}=\frac{1}{4}\)