Tìm ƯCLN của
a) 32; 128 b) 42 ; 30 c) 16; 32; 128 d) 42; 30; 20
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C=1/2+1/4+1/8+1/16+1/32+1/64+1/128
C=1-1/2+1/2-1/4+1/4-1/8+1/8-1/16+1/16-1/32+1/32-1/64+1/64-1/128
C=1-1/128
C=127/128
D=1/2+1/6+1/12+1/20+1/30+1/42
D=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7
D=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
D=1/1-1/7
D=6/7
\(B=\frac{6}{1\cdot3}+\frac{6}{3\cdot5}+\cdot\cdot\cdot+\frac{6}{97\cdot99}\)
\(\Rightarrow B=3\cdot\left(\frac{2}{1\cdot3}+\cdot\cdot\cdot+\frac{2}{97\cdot99}\right)\)
\(\Rightarrow B=3\cdot\left(1-\frac{1}{3}+\cdot\cdot\cdot+\frac{1}{97}-\frac{1}{99}\right)\)
\(\Rightarrow B=3\cdot\left(1-\frac{1}{99}\right)\)
\(\Rightarrow B=3\cdot\frac{98}{99}\)
\(\Rightarrow B=\frac{98}{33}\)
\(A=\frac{1}{2}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{42}\)
\(\Rightarrow A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdot\cdot\cdot+\frac{1}{6\cdot7}\)
\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\cdot\cdot\cdot+\frac{1}{6}-\frac{1}{7}\)
\(\Rightarrow A=1-\frac{1}{7}\)
\(\Rightarrow A=\frac{6}{7}\)
a: \(A=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+...+\left(\dfrac{1}{2}\right)^7\)
=>\(2\cdot A=1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^6\)
=>\(2A-A=1-\left(\dfrac{1}{2}\right)^7=1-\dfrac{1}{128}=\dfrac{127}{128}\)
=>\(A=\dfrac{127}{128}\)
b: \(B=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10\cdot11}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)
\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)
Tìm x :
a. -x + 17 = -12
x = (-12) -17
x = -29
b. -30 + (32-x) = 10
32-x = 10-(-30)
32-x = 40
x = 32 - 40
x = -8
c. \(|2x-1|\) = 7
=> 2x - 1 = 7 hoặc => 2x - 1 = -7
=> x = 4 => x = -3
d. \(|x+3|\) - 5 = 7
\(|x+3|\) = 7 + 5
\(|x+3|\) = 12
=> x + 3 = 12 hoặc => x + 3 = -12
=> x = 12 - 3 => x = (-12) - 3
=> x = 9 => x = -15
e. 16 - ( 42 + x ) = 50
42 + x = 16 - 50
42 + x = -34
x = (-34) - 42
x = -76
g. 128 - 3 . ( x + 4 ) = 23
3 . ( x + 4 ) = 128 - 23
3 . ( x + 4 ) = 105
x + 4 = 105 : 3
x + 4 = 35
x = 35 - 4
x = 31
A, -20+ (x-16) = -32
-20 +x -16 = -32
-36 + x = -32
x = -32 - (-36)
x = 4
Vậy x= 4
B, -42 - 7x= -14
-7x=-42-(-14)
-7x = -28
x = -28 : (-7)
x = 4
Vậy x= 4
c, 26+|𝑥−15|=30
| x -15| = 4
TH1: x - 15= 4
x = 19
TH2: x - 15 = -4
x= 11
vậy.........