1.

Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{a}{2}=\frac{b}{3}=\frac{c}{4}$

$=\frac{a}{2}=\frac{2b}{6}=\frac{3c}{12}=\frac{a+2b+3c}{2+6+12}=\frac{-20}{20}=-1$

$\Rightarrow a=2(-1)=-2; b=3(-1)=-3; c=4(-1)=-4$

2.

$S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{9900}$
$=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}$

$=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+....+\frac{100-99}{99.100}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}$

$=1-\frac{1}{100}=\frac{99}{100}$

a) Ta có : \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\)

\(\Rightarrow\dfrac{a}{2}=\dfrac{2b}{6}=\dfrac{3c}{12}=\dfrac{a+2b+3c}{2+6+12}=\dfrac{-20}{20}=-1\)

\(\Rightarrow\left\{{}\begin{matrix}a=\left(-1\right)\cdot2=-2\\b=\dfrac{\left(-1\right).6}{2}=-3\\c=\dfrac{\left(-1\right).12}{3}=-4\end{matrix}\right.\)

b) Ta có : \(S=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}\)

\(=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

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

\(=1-\dfrac{1}{100}=\dfrac{99}{100}\).

Vậy : \(S=\dfrac{99}{100}.\)

a)\(\dfrac{a}{2}=\dfrac{2b}{6}=\dfrac{3c}{12}=\dfrac{a+2b+3c}{2+6+12}=-\dfrac{20}{20}=-1\)

\(\left\{{}\begin{matrix}\dfrac{a}{2}=-1\Leftrightarrow a=-2\\\dfrac{b}{3}=-1\Leftrightarrow b=-3\\\dfrac{c}{4}=-1\Leftrightarrow c=-4\end{matrix}\right.\)

b)\(S=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{9900}\\ =\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\\ =\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\\ =1-\dfrac{1}{100}=\dfrac{99}{100}\)

hihihivi

a) (x-3).11=(x-7).10

=>11x-33=10x-70

=>11x-10x=-70+33

=>x= -37

1. Ư (-2) = { -1;-2; 1;2 }

Ư( 4) = { -1: -2: -4: 1: 2:4}

Ư(13)= { 1: 13: -1: -13}

Ư(15) ={ 1: 15: 3:5: -1: -3: -5: -15}

Ư(1) ={ 1: -1}

2. B(2) = { 0;2; 4; 6;8}

B(-2)= { 0; -2; -4; -6; -8}

3. a) Có thể lập được 15 tổng dạng ( a+b)....

b) Bn tự tính tổng các số đó r chia cho 3 xem số nào chia được nha

Bài 1:

a,Ta có:\(\frac{3}{5}=\frac{3\times2}{5\times2}=\frac{6}{10}\)      (1)

              \(\frac{4}{5}=\frac{4\times2}{5\times2}=\frac{8}{10}\)       (2)

Từ (1) và (2)=> Một phân số tối giản nằm giữa hai phân số trên là:\(\frac{7}{10}\)

b,Ta có:\(\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}\)

               \(\frac{4}{5}=\frac{4\times3}{5\times3}=\frac{12}{15}\)

=> hai phân số ở giữa là:\(\frac{10}{15}=\frac{2}{3};\frac{11}{12}\)

hộ C1: Tìm x biết

a 2x-35=15

=>2x=15+35=50

=>x=25

b 3x+17=2

=>3x=2-17=-15

=>x=5

c x+3/15=1/3

x=1/3-3/15=2/15

d x-12/4=1/2

x=1/2+12/4=7/2

a. 2x-35=15

    2x=15+35

    2x=50

      x=50:2

      x=25

Vậy x=25

b. 3x+17=2

    3x=2-17

    3x=-15

      x=-15:3

      x=-5

Vậy x=-5

c. \(\frac{x+3}{15}=\frac{1}{3}\)

\(\Rightarrow3x+9=15\)

      \(3x=15-9\)

      \(3x=6\)

         \(x=6:3\)

         \(x=3\)

Vậy x=3

d. \(\frac{x-12}{4}=\frac{1}{2}\)

\(\Rightarrow2x-24=4\)

      \(2x=4+24\)

      \(2x=28\)

         \(x=28:2\)

         \(x=14\)

Vậy x=14

C1

a, 2x - 35 = 15 

2x = 15 + 35

2x = 50

x = 25

b, 3x + 17 = 2

3x = 2 - 17

3x = -15

x = -3

c, \(\frac{x+3}{15}=\frac{1}{3}\)

\(\frac{3x+3}{45}=\frac{15}{45}\)

3x + 3 = 15

3x = 15 - 3

3x = 12

x = 4

d, \(\frac{x-12}{4}=\frac{1}{2}\)

\(\frac{2x-24}{8}=\frac{4}{8}\)

2x - 24 = 4

2x = 4 + 24

2x = 28 

x = 14

B2

a , \(\frac{-315}{540}=\frac{-7}{12}\)  

b, \(\frac{25\times13}{26\times35}=\frac{5}{14}\)

c, \(\frac{6\times9-2\times17}{63\times3-119}=\frac{2}{7}\)

d, \(\frac{x-12}{4}=\frac{1}{2}\)

\(\frac{2x-24}{8}=\frac{4}{8}\)

2x - 24 = 4

2x = 28

x = 14 ( giống câu d bài 1 )

B3 

a, \(\frac{6}{7}=\frac{6\times5}{7\times5}=\frac{30}{35}\)

\(\frac{3}{5}=\frac{3\times7}{5\times7}=\frac{21}{35}\)

b, \(\frac{3}{-2}\)và \(\frac{-1}{-4}=\frac{1}{4}\)

\(\frac{3}{-2}=\frac{3\times-2}{-2\times-2}=\frac{-6}{4}\)

c, \(\frac{7}{-10}=\frac{7\times8}{-10\times8}=\frac{56}{-80}=\frac{-56}{80}\)

\(\frac{7}{8}=\frac{7\times-10}{8\times-10}=\frac{-70}{-80}=\frac{70}{80}\)

d, \(\frac{14}{21}=\frac{14\times72}{21\times72}=\frac{1008}{1512}\)

\(\frac{-60}{72}=\frac{-60\times21}{72\times21}=\frac{-1260}{1512}\)