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a)
\(=\frac{7\cdot7\cdot8\cdot8\cdot9\cdot9\cdot10\cdot10\cdot11\cdot11}{6\cdot8\cdot7\cdot9\cdot8\cdot10\cdot9\cdot11\cdot10\cdot12}\)
\(=\frac{7\cdot11}{6\cdot12}\)
\(=\frac{77}{72}\)
b)
\(=1+\frac{1}{6}+1+\frac{1}{12}+1+\frac{1}{20}+1+\frac{1}{30}+1+\frac{1}{42}+1+\frac{1}{56}\)
\(=6+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)
\(=6+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)
\(=6+\frac{1}{2}-\frac{1}{8}\)
\(=6+\frac{3}{8}\)
\(=\frac{51}{8}\)
Chia thành...a và b nhé.
Bg
a)Ta có: \(\frac{49}{48}.\frac{64}{63}.\frac{81}{80}.\frac{100}{99}.\frac{121}{120}\)
= \(\frac{49.64.81.100.121}{48.63.80.99.120}\)
= \(\frac{7.7.8.8.9.9.10.10.11.11}{6.8.7.9.8.10.9.11.10.12}\)
= \(\frac{7.11}{6.12}\) (chịt tiêu trên dưới)
= \(\frac{77}{72}\)
b) Ta có: \(\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}\)
Có 6 số hạng (đếm)
= \(1+\frac{1}{6}+1+\frac{1}{12}+1+\frac{1}{20}+1+\frac{1}{30}+1+\frac{1}{42}+1+\frac{1}{56}\)
= \(1+1+...+1+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
= \(1.6+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
= \(6+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
= \(6+\frac{1}{2}-\frac{1}{8}\)
= \(\frac{13}{2}-\frac{1}{8}\)
= \(\frac{51}{8}\)
Hơi dài....
![](https://rs.olm.vn/images/avt/0.png?1311)
a) 1 < x < 10 3 = > x ∈ {2;3}
b) 2 5 < x ≤ 23 6 = > x ∈ {1;2;3}
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= 152 - 2. ( 56 - 48 : 8 )
= 152 - 2. (56 - 6 )
= 152 - 2. 50
= 152 - 100
= 52
Hk tốt
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a) Đặt A = 1 + 4 + 7 + ..... + 100
Số số hạng của A là :
(100 - 1) : 3 + 1 = 34
Tổng A có giá trị là :
(100 + 1) x 34 : 2 = 1717
Thay A vào đề bài ta có : x + 1717 = 1996
=> x = 1996 - 1717
=> x = 279
b) 786 + (x + 2 + 4 + ......... + 48 + 50) = 2007
Đặt B = 2 + 4 + ......... + 50
Số số hạng của B là :
(50 - 2) : 2 + 1 = 25 (số)
Tổng B có giá trị là :
(50 + 2) x 25 : 2 = 650
Thay B vào đề bài ta có : 786 + x + 650 = 2007
=> x + 1436 = 2007
=> x = 571
Vậy x = 571
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c: \(2448:\left[199-23-6\right]\)
\(=2448:90\)
\(=\dfrac{136}{5}\)
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a) \(170-x+56=100\)
\(\Rightarrow170-x=44\)
\(\Rightarrow x=170-44\)
\(\Rightarrow x=126\)
b) \(55:x+92,3=97,3\)
\(\Rightarrow55:x=97,3-92,3\)
\(\Rightarrow55:x=5\)
\(\Rightarrow x=\dfrac{55}{5}=11\)
c) \(\left(7x-24\right)-13,5=305,5\)
\(\Rightarrow7x-24=319\)
\(\Rightarrow7x=343\)
\(\Rightarrow x=\dfrac{343}{7}=49\)
a) 170-x+56=100
170 - x = 100 - 56
170 - x= 44
x= 170 - 44
x= 126
b)55:x+92,3=97,3
55:x = 97,3 - 92,3
55:x=5
x=55:5
x=11
c) (7.x-24)-13,5=305,5
(7.x - 24) = 305,5 + 13,5
7.x - 24= 319
7.x= 319 + 24
7.x= 343
x= 343:7
x= 49
![](https://rs.olm.vn/images/avt/0.png?1311)
x-6-(48-24x2:6-3)=100
x-6-(48-8-3)=100
x-6-37=100
x-6=137
x=137+6=143
Vậy x=143
20-[7x(X-3)+4]=2
7x(X-3)+4=20-2
7x(X-3)+4=18
7x(X-3)=14
X-3=14:7
X-3=7
X=7+3=10
Vậy X=10
[(6.X-39):3].28=5628
(6.X-39):3=5628:28
(6.X-39):3=201
6.X-39=201.3=603
6.X=603+39
6.X=642
X=642:6=107
Vậy x=107
1) \(x-6-\left(48-24.2:6-3\right)=100\Rightarrow x-6-\left(48-8-3\right)=100\)
\(\Rightarrow x-6-37=100\Rightarrow x=100+37+6=143\)
2) \(20-\left[7\left(x-3\right)+4\right]=2\Rightarrow7\left(x-3\right)+4=20-2=18\)
\(\Rightarrow7\left(x-3\right)=18-4=14\Rightarrow x-3=14:7=2\Rightarrow x=2+3=5\)
3) \(\left[\left(6x-39\right):3\right].28=5628\Rightarrow\left(6x-39\right):3=5628:28=201\)
\(\Rightarrow6x-39=201.3=603\Rightarrow6x=603+39=642\Rightarrow x=642:6=107\)
56-48:(x-7)=100:2
56-48:(x-7)=50
48:(x-7)=56-50
48:(x-7)=6
x-7 = 48:6
x-7=8
x=7+8
x=15
\(2\times\left[56-48:\left(x-7\right)\right]=100\)
\(\Rightarrow56-48:\left(x-7\right)=100:2\)
\(\Rightarrow56-48:\left(x-7\right)=50\)
\(\Rightarrow48:\left(x-7\right)=56-50\)
\(\Rightarrow48:\left(x-7\right)=6\)
\(\Rightarrow x-7=48:6\)
\(\Rightarrow x-7=8\)
\(\Rightarrow x=8+7\)
\(\Rightarrow x=15\)
Vậy $x=15$