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\(M=\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}+\frac{73}{72}\)
\(\Rightarrow M=\left(1+\frac{1}{12}\right)+\left(1+\frac{1}{20}\right)+\left(1+\frac{1}{30}\right)+\left(1+\frac{1}{42}\right)+\left(1+\frac{1}{56}\right)+\left(1+\frac{1}{72}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right)\)
\(\Rightarrow M=6+\left(\frac{1}{3}-\frac{1}{9}\right)=6+\left(\frac{3}{9}-\frac{1}{9}\right)\)
\(\Rightarrow M=6+\frac{2}{9}=\frac{54}{9}+\frac{2}{9}=\frac{56}{9}\)
a,
15^12=(3*5)^12=3^12*5^12
81^3*125^5=(3^4)^3*(5^3)^5=3^12*5^15
Vì 12<15 suy ra 5^12<5^15
Suy ra 3^12*5^12<3^12*5^15
\(a.81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{12}.5^{15}=3^{12}.5^{12}.5^3=\left(3.5\right)^{12}.5^3=15^{12}.5^3>15^{12}\)
\(b.4^{20}.81^{12}=\left(2^2\right)^{20}.\left(9^2\right)^{12}=2^{40}.9^{24}=2^{20}.2^{20}.9^{20}.9^4=\left(2.9\right)^{20}.2^{20}.9^4=18^{20}.2^{20}.9^4>18^{20}\)
\(c.73^{75}=\left(73^3\right)^{25}=389017^{25}\)
\(107^{50}=107^{2.50}=\left(107^2\right)^{25}=11449^{25}\)
Vì \(389017^{25}>11449^{25}\Rightarrow73^{75}>107^{50}\)
1/ \(-12;-7;-1;0;4;10;\left|-18\right|\)
2/ \(-13;-5;0;+3;\left|+4\right|;12;\left|-15\right|\)
3/ \(\left|-26\right|;19;-\left(-12\right);0;-4;-\left|35\right|\)
4/ \(-\left(-73\right);\left|+7\right|;4;\left|-1\right|;0;+\left(-5\right);-\left(+22\right)\)
Bài 20:
*Tăng dần
1/ -12; -7; -1; 0; +4; 10; |-18|
2/ -13; -5; 0; +3; |+4|; 12; |-15|
*Giảm dần
3/ |-26|; +19; -(-12); 0; -4; -|-35|
4/ -(-73); | +7|; 4; |-1|; 0; +(-5); -(+22)
Chúc bạn học tốt !!!
2x+7/6+13/12+21/20+31/30+43/42+57/56+73/72+91/90=10
2x+1+1/6+1+1/12+1+1/20+1+1/30+1+1/42+1+1/56+1+1/72+1+1/90=10
2x+(1+1+1+1+1+1+1+1)+(1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10)=10
2x+8+(1-1/2+1/2-1/3+...+1/9-1/10)=10
2x+1-1/10=10-8
2x+9/10=2
2x=2-9/10
2x=11/10
x=11/10/2
x=11/20
= (-12).73 + 20 .(-12) + 7.(-12)
= (-12).(73+20+7)
=(-12) x 100
=-1200
các bạn cho mình vài li-ke cho tròn 510 với