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\(=\dfrac{3^{15}\cdot2^{22}+2^8\cdot2^{16}\cdot3^{16}}{2\cdot3^{18}\cdot2^{21}-7\cdot3^{15}\cdot2^{23}}\)
\(=\dfrac{3^{15}\cdot2^{22}\left(1+2^2\cdot3\right)}{3^{15}\cdot2^{22}\left(3^3-7\cdot2\right)}=\dfrac{1+4\cdot3}{27-14}=1\)
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=1.3/2^2×2.4/3^2×3.5/4^2×...×29.31/30^2
=1.2.3....29/2.3.4...30×3.4.5....31/2.3.4...30
=1/30×31/2
=31/60
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a, ( 1/2 + 1) . ( 1/3 + 1) . (1/4 + 1) ... ( 1/999 + 1)
= 3/2 . 4/3 . 5/4 . 1000/999
= 1/2 . 1/1 . 1/1 ... 1000/1
= 1000/2
= 500
b, (1/2-1) . (1/3-1) . (1/4-1) ... (1/1000-1)
= -1/2 . (-2)/3 . (-3)/4 ... (-999)/1000
= (-1)/1 . (-1)/1 . (-1)/1 ... (-1)/1000
= (-1)/1000
c, 3/2^2 . 8/3^2 . 15/4^2 ... 99/10^2
= 1.3/2.2 * 2.4/3.3 * 3.5/4.4***9.11/10.10
=( 1.2.3...99).(3.4.5...11)/(2.3.4....10).(2.3.4...10)
= 1.11/2.10
= 11/20
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\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}.........\frac{899}{30^2}\)
A= \(\frac{1.3.2.4.3.5...29.31}{2.2.3.3...30.30}\)
A=\(\frac{\left(2.3...29.30\right)\left(3.4.5...29.31\right)}{\left(2.3.4...30\right)\left(2.3.4...30\right)}\)
A=\(\frac{31}{2.30}\)
A=\(\frac{31}{60}\)
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=(1-2)-(3-4)+(5-6)-(7-8)+...+(2021-2022)-2023
=(-1)-(-1)+(-1)-...+(-1)-2023
=0-2023
=-2023
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Ta có : S = (-1)+2+(-3)+4+(-5)+...+(-99)+100
= -1 + (-1) + (-1) +...+ (-1) (50 số -1)
= -50
số số hạng là:(100-1):1+1=100 số
S=-1+(-1)+..+(-1)=-50
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Câu 11:
(\(\dfrac{11}{4}\). \(\dfrac{-5}{9}\) - \(\dfrac{4}{9}\).\(\dfrac{11}{4}\)).\(\dfrac{8}{33}\)
= \(\dfrac{11}{4}\).(\(\dfrac{-5}{9}\) - \(\dfrac{4}{9}\)). \(\dfrac{8}{33}\)
= \(\dfrac{11}{4}\).(-1).\(\dfrac{8}{33}\)
= - \(\dfrac{2}{3}\)
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(x+1) + (x+2) + (x+3) + (x+4) + ...+ (x+30) = 795
x.30 + (1+30).30 : 2 = 795
30x + 465 = 795
30x = 330
x = 11
( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) + .... + ( x + 30 ) = 795
( x + x + x + x + ...+ x ) + ( 1 + 2 + 3 + 4 + ... + 30 ) = 795
Tổng số các số hạng là : ( 1 + 30 ) . 30 : 2 = 465
=> x. 30 + 465 = 795
=> x . 30 = 330
=> x = 11
Vậy x = 11