A=5/20+5/30+5/42+...+5/240

A=5/4.5+5/5.6+5/6.7+...+5/15.16

A=5.(1/4.5+1/5.6+1/6.7+...+1/15.16)

A=5.(1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16)

A=5.(1/4-1/16)

A=5.3/16

A=15/16

Vậy A=15/16

\(a)A=\dfrac{2}{20}+\dfrac{2}{30}+\dfrac{2}{42}+...+\dfrac{2}{240}\)

\(A=2\left(\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+...+\dfrac{1}{15.16}\right)\)

\(A=2\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{15}-\dfrac{1}{16}\right)\)

\(A=2\left(\dfrac{4}{16}-\dfrac{1}{16}\right)\)

\(A=\dfrac{2.3}{16}\)

\(=\dfrac{3}{8}\)

\(b)B=\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}\)

\(B=\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+...+\left(1-\dfrac{1}{56}\right)\)

\(B=6-\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{7.8}\right)\)

\(B=6-\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)\)

\(B=6-\left(\dfrac{4}{8}-\dfrac{1}{8}\right)\)

\(B=\dfrac{48}{8}-\dfrac{3}{8}\)

\(B=\dfrac{45}{8}\)

a, \(15:\left(x+2\right)=3\Leftrightarrow x+2=3\Leftrightarrow x=1\)

b, \(20:\left(x+1\right)=2\Leftrightarrow x+1=10\Leftrightarrow x=9\)

c, \(240:\left(x-5\right)=2^2.5^2-20=80\Leftrightarrow x-5=3\Leftrightarrow x=8\)

d, \(96-3\left(x+1\right)=42\Leftrightarrow3\left(x+1\right)=54\Leftrightarrow x+1=18\Leftrightarrow x=17\)

a) 15 : (x + 2) = 3

x + 2 = 15 : 3

x + 2 = 5

x = 5 – 2 = 3

b) 20 : (1 + x) = 2

1 + x = 20 : 2

1 + x = 10

x = 10 – 1 = 9

c) 240 : (x – 5) = 2².5² – 20

240 : (x – 5) = 4.25 – 20

240 : (x - 5) = 100 – 20

240 : (x - 5) = 80

x – 5 = 240 : 80

x – 5 = 3

x = 3 + 5 = 8

d) 96 - 3(x + 1) = 42

3(x + 1) = 96 – 42

3(x + 1) = 54

x + 1 = 54 : 3

x + 1 = 18

x = 18 – 1

x = 17

\(15\div\left(x+2\right)=3\)                                           \(20\div\left(1+x\right)=2\)

\(x+2=15\div3\)                                               \(1+x=20\div2\)

\(x+2=5\)                                                       1+x=10

x = 5 - 2                                                           x=9

x = 3

\(240\div\left(x-5\right)=2^2\cdot5^2-20\)                                \(96-3\left(x+1\right)=42\)

\(240\div\left(x-5\right)=80\)                                              \(3\left(x+1\right)=96-42\)

\(x-5=240\div80\)                                                 \(3\left(x+1\right)=54\)

x-5=3                                                                    \(x+1=54\div3\)

x=8                                                                        x+1=18

                                                                              x=17

a,\(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}=\frac{29}{45}\)

\(\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)=\frac{29}{45}\)

\(\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{29}{45}\)

\(\frac{7}{x}+\frac{8}{45}=\frac{29}{45}\)

\(\frac{7}{x}=\frac{29}{45}-\frac{8}{45}=\frac{21}{45}\)

\(\frac{7}{x}=\frac{7}{15}\)

=> x = 15

b,\(\frac{x}{2008}-\left(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+....+\frac{2}{240}\right)=\frac{5}{8}\)

\(\frac{x}{2008}-2\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)=\frac{5}{8}\)

\(\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+....+\frac{1}{15}-\frac{1}{16}\right)=\frac{5}{8}\)

\(\frac{x}{2008}-2\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{5}{8}\)

\(\frac{x}{2008}-2.\frac{3}{16}=\frac{5}{8}\)

\(\frac{x}{2008}-\frac{3}{8}=\frac{5}{8}\)

\(\frac{x}{2008}=\frac{5}{8}+\frac{3}{8}=1=\frac{2008}{2008}\)

=> x = 2008

Bài 1.

\(20:x-5=5\\ 20:x=5+5\\ 20:x=10\\ x=20:10\\ x=2\\ 20-18:x=18\\ 18:x=20-18\\ 18:x=2\\ x=18:2\\ x=9\\ 42:x-5=2\\ 42:x=2+5\\ 42:x=7\\ x=42:7\\ x=6\\ 38-30:x=35\\ 30:x=38-35\\ 30:x=3\\ x=30:3\\ x=10\\ 30-x:4=22\\ x:4=30-22\\ x:4=8\\ x=8\times4\\ x=32\)

Bài 2. 

\(72+19+5=91+5=96\\ 32+15-9=47-9=38\\ 69-\left(45+5\right)=69-50=19\)

Bài 3. Bài giải

Số lớn nhất có \(3\) chữ số là: \(999\)

Số chẵn bé nhất có \(3\) chữ số là: \(100\)

Hiệu hai số là:

\(999-100=899\)

Đáp số: \(899\)

Bài 1: 

a. 20 : x = 5 + 5 

20 : x = 10 

x = 20 : 10 = 2

b.20 - 18 : x = 18 

18 : x = 20 - 18 

18 : x = 2

x = 18 : 2 = 9 

c. 42 : x = 2 + 5 

42 : x = 7 

x = 42 : 7 = 6 

d. 38 - 30 : x = 35 

30 : x = 38 - 35 

30 : x = 3 

x = 30 : 3 = 10 

e. x : 4 = 30 - 22 

x : 4 = 8 

x = 8 x 4 = 32 

Bài 2: 

a. 72 + 19 + 5 = 96 

b. 32 + 15 - 9 = 38 

c. 69 - 50 = 19 

Bài 3: 

Só lớn nhất có  chữ số là: 999 

Số chẵn bé nhất có chữ số là: 100 

Hiệu 2 số đó là: 999 - 100 = 899 

Con yêu bà rất nhiều và con hứa con có cái gì con đều cho bà tất cả 

bà cần cái gì con và bố con sẽ mua cho

\(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+\dfrac{5}{42}+...+\dfrac{5}{110}\)

\(=\dfrac{5}{1.2}+\dfrac{5}{2.3}+\dfrac{5}{3.4}+\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{5}{6.7}+...+\dfrac{5}{10.11}\)

\(=\dfrac{5}{1}-\dfrac{5}{2}+\dfrac{5}{2}-\dfrac{5}{3}+\dfrac{5}{3}-\dfrac{5}{4}+\dfrac{5}{4}-\dfrac{5}{5}+...+\dfrac{5}{10}-\dfrac{5}{11}\)

\(=\dfrac{5}{1}-\dfrac{5}{11}=\dfrac{50}{11}\)

=5(1/2+1/6+1/12+1/20+1/30+1/42+...+1/110)

=5(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/10.11)

=5(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/10-1/11)

=5(1-1/11)=5.10/11=50/11

\(\dfrac{5}{2}+\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+\dfrac{5}{42}+....+\dfrac{5}{110}\)

\(=\dfrac{5}{1.2}+\dfrac{5}{2.3}+\dfrac{5}{3.4}+\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{5}{6.7}+....+\dfrac{5}{10.11}\)

\(=\dfrac{5}{1}-\dfrac{5}{2}+\dfrac{5}{2}-\dfrac{5}{3}+\dfrac{5}{3}-\dfrac{5}{4}+\dfrac{5}{4}-\dfrac{5}{5}+....+\dfrac{5}{10}-\dfrac{5}{11}\)

\(=\dfrac{5}{1}-\dfrac{5}{11}\)

\(=\dfrac{50}{11}\)

` 45 : ( 5+4 ) = 45 : 9 =5`

` 8 xx ( 11-6) = 8 xx 5 = 40 `

` 42 - ( 42-5) = 42-37=5`

a) 45 : (5 +4) = 45 : 9

                      = 5

b) 8 x (11 - 6) = 8 x 5

                      = 40

c) 42 - (42 - 5) = 42 - 37 

                        = 5