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1.2.3...2013-1.2.3...2012-1.2.3...20122= (1.2.3...2013-1.2.3...2012) - 1.2.3...20122 = [1.2.3...2012(2013-1)] - 1.2.3...20122 = 1.2.3...2012.2012 - 1.2.3...20122 = 1.2.3...20122 - 1.2.3...20122 = 0
1 . 2 . 3 . ...... 2012 . ( 2013 - 1 - 2012 )
1 . 2 . 3 ..........2012 . ( 0 ) = 0
a) 2012 - ( 304 + 2012 ) + ( 2013 + 304 )
= 2012 - 304 - 2012 + 2013 + 304
= 2012 + ( - 304 ) + ( - 2012 ) + 2013 + 304
= [ 2012 + ( - 2012 ) ] + [ ( - 304 ) + 304 ] + 2013
= 0 + 0 + 2013
= 2013
b) \(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)
\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(3^2.2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{3^{24}.2^{12}.5^{12}.2^9.3^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{3^{27}.5^{12}.2^{21}}\)
\(=\frac{3}{5^2}=\frac{3}{25}\)
a) 2012 - ( 304 + 2012 ) + (2013 + 304 )
= 2012 - 304 +2012 + 2013 + 304
= ( 2012 - 2012 ) + ( 304 + 304 ) + 2013
= 0 + 608 + 2013
= 2621
Chờ một chút để minh suy nghĩ
Câu 2:
a: \(=9\cdot8-72:4=72-18=54\)
b: \(=125\cdot26+125\cdot32+125\cdot42\)
\(=125\left(26+32+42\right)=125\cdot100=12500\)
c: \(=5871:\left(928-825\right)+1=5871:103+1=57+1=58\)
d: \(=2012+78-178-2012=-100\)
Co quy luat nay ne em: 1+2=3=2.3:2; 1+2+3=6=3.4:2;...;1+2+3+...+2012=2012.2013:2
Suy ra ta co:
Mau so cua D=1 + 1/(2.3:2) + 1/(3.4:2) + 1/(4.5:2) + .... + 1/(2012.2013:2)
=1 + 2/2.3 + 2/3.4 + 2/4.5 + .... + 2/2012.2013
= 2.[1/2 + 1/2.3 + 1/3.4 + 1/4.5 + .... + 1/2012.2013]
=2.[1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + ..... + 1/2012.2013]
=2.[1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +....+1/2012 - 1/2013
=2[1 - 1/2013]
=2.2012/2013
Vay D= 2.2012 / (2.2012:2013)=2013
a, 67,8 x 2012 + 33,2 × 2012-2012
= 67,8×2012+33,2×2012-2012×1
=2012×(67,8+33,2-1)
=2012×100
=201200
b, 5/11 + 7/9 + 2/9 + 6/11 + 7/15
=( 5/11 + 6/11) + ( 7/9 +2/9) +7/15
=1 + 1 + 7/15
=2 + 7/15
=37/15
a, 67,8 x 2012 + 33,2 × 2012-2012
= 67,8×2012+33,2×2012-2012×1
=2012×(67,8+33,2-1)
=2012×100
=201200
b, 5/11 + 7/9 + 2/9 + 6/11 + 7/15
=( 5/11 + 6/11) + ( 7/9 +2/9) +7/15
=1 + 1 + 7/15
=2 + 7/15
=37/15