Tính : 10^2+11^2+12^2+...+19^2+20^2 (mong được giải chi tiết ạ)
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a: \(=\dfrac{-39+19+10}{12}=\dfrac{-10}{12}=\dfrac{-5}{6}\)
b: \(=\dfrac{2^{30}\cdot3^{16}\cdot7-2^{34}\cdot3^{15}}{2^{28}\cdot3^{21}-2^{28}\cdot3^{17}}\)
\(=\dfrac{2^{30}\cdot3^{15}\left(3\cdot7-2^4\right)}{2^{28}\cdot3^{17}\left(3^4-1\right)}=\dfrac{2^2}{3^2}\cdot\dfrac{21-16}{80}=\dfrac{4}{9}\cdot\dfrac{5}{80}\)
\(=\dfrac{20}{720}=\dfrac{1}{36}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2 + 5/6 + 11/12 + ... + 89/90
= (1 - 1/2) + (1 - 1/6) + (1 - 1/12) + ... + (1 - 1/90)
= (1 - 1/1.2) + (1 - 1/2.3) +(1 - 1/3.4) + ... + (1 - 1/9.10)
= (1 + 1 + 1 + ... + 1) - (1/1.2 + 1/2.3 + 1/3.4 + ... + 1/9.10)
9 số 1
= 9 - (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10)
= 9 - (1 - 1/10)
= 9 - 9/10
= 90/10 - 9/10
= 81/10
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a) x+3=12
x=12-3
x=9
b)(x-3):2=514:512
=>(x-3):2=52
=>(x-3):2=25
=>x-3=25.2
=>x-3=50
=>x=50+3
=>x=53
c)4x+3x=30-20:10
=>x(4+3)=30-2
=>7x=28
=>x=28:7
=>x=4
d)2x-138=23.32
=>2x-138=8.9
=>2x-138=72
=>2x=72+138
=>2x=210
=>x=210:2
=>x=105
a) x + 3 = 12
x = 12 - 3
x = 9
b) ( x - 3 ) : 2 = 514 : 512
( x - 3 ) : 2 = 514-12
( x - 3 ) : 2 = 52
( x - 3 ) : 2 = 25
x - 3 = 50
x = 53
c) 4x + 3x = 30 - 20 : 10
7x = 28
x = 4
d) 2x - 138 = 23 x 32
2x - 138 = 8 x 9
2x - 138 = 72
2x = 210
x = 105
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\frac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(2^2.3\right)^{10}}\)
\(=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\)
\(=\frac{2^{18}.3^8.\left(2.3+3.5\right)}{2^{18}.3^9.\left(2+2^2.3\right)}\)
\(=\frac{6+15}{3.\left(2+12\right)}\)
\(=\frac{21}{3.14}=\frac{21}{42}=\frac{1}{2}\)
\(A=\frac{2^{19}\cdot3^9+3\cdot5\cdot2^{18}\cdot3^8}{2^9\cdot3^9\cdot2^{10}+4^{10}\cdot3^{10}}=\frac{2^{18}\cdot3^9\times\left(2+5\right)}{2^{19}\cdot3^9\times\left(1+6\right)}=\frac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{5}{-6}=\dfrac{-55}{66};\dfrac{-10}{11}=\dfrac{-60}{66}\Rightarrow\dfrac{-55}{66}>\dfrac{-60}{66}\Rightarrow\dfrac{5}{-6}>\dfrac{-10}{11}\\ \dfrac{-3}{20}=\dfrac{-45}{300};\dfrac{2}{-15}=\dfrac{-40}{300}\Rightarrow\dfrac{-45}{300}< \dfrac{-40}{300}\Rightarrow\dfrac{-3}{20}< \dfrac{2}{-15}\\ -0,305>-0,36\)
\(^\circ\) \(\dfrac{5}{-6}\) và \(\dfrac{-10}{11}\)
Ta có \(:\)
\(\dfrac{5}{-6} = \dfrac{ 5 . 11 }{ -6 . 11 } = \dfrac{ 55 }{ -66} \)
\(\dfrac{-10}{11} = \dfrac{-10 . ( -6 )}{11.(-6)} = \dfrac{60}{-66}\)
Do \(55 < 60\)
\(=> \dfrac{55}{-66} > \dfrac{60}{-66}\)
Vậy \(\dfrac{55}{-66} > \dfrac{60}{-66}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
10/29+11/29+12/29+...+19/29
=10+11+12+13+14+15+=16+17+18+19/29
=145/29
![](https://rs.olm.vn/images/avt/0.png?1311)
a: =-5/9-4/9+8/15+7/15-2/11=-2/11
b: =10/17+7/17-5/13-8/13+11/25
=11/25
c: =(9/12-2/12)*3/2=7/12*3/2=21/24=7/8
d: =(31/10-25/10)*3-2
=3/5*3-2
=9/5-2
=-1/5