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1-3+5-7+...+21-23
=(1-3)+(5-7)+...+(21-23)
Tổng số cặp là:
[(23-1):2+1]:2=6
Nháp: [(23-1):2+1]:2=(22:2+1):2=12:2=6
=1-3=-2=-2*6=-12
Đây nha bạn.
Chúc bạn học tốt!
\(1-3+5-7+...+21-23\)
\(=\left(1+5+9+13+17+21\right)-\left(3+7+11+15+19+23\right)\)
\(=\left[\left(21-1\right):2+1\right].\left(21+1\right):2-\left[\left(23-3\right):2+1\right].\left(23+3\right):2\)
\(=11.11-11.13\)
\(=121-143\)
\(=-22\)
a) \(\left(\left(\frac{-12}{16}\right)+\frac{7}{14}\right)-\left(\frac{1}{13}-\frac{3}{13}\right)\) \(=\left(\left(\frac{-3}{4}\right)+\frac{1}{2}\right)-\left(\frac{-2}{13}\right)\) \(=\left(\frac{-2}{8}\right)-\left(\frac{-2}{13}\right)\) \(=\left(\frac{-10}{104}\right)\) \(=\left(\frac{-5}{72}\right)\) | b) \(\frac{10}{11}+\frac{4}{11}:4-\frac{1}{8}\) \(=\frac{10}{11}+\frac{4}{11}:\frac{4}{1}-\frac{1}{8}\) \(=\frac{10}{11}+\frac{4}{11}\cdot\frac{1}{4}-\frac{1}{8}\) \(=\frac{10}{11}+\frac{1}{11}-\frac{1}{8}\) \(=\frac{11}{11}-\frac{1}{8}\) \(=1-\frac{1}{8}\) \(=\frac{7}{8}\) |
HT
\(A=5+5^2+5^3+5^4+...+5^{11}+5^{12}\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{11}+5^{12}\right)\)
\(=\left(5+5^2\right)+5^2\left(5+5^2\right)+...+5^{10}\left(5+5^2\right)\)
\(=30\left(1+5^2+...+5^{10}\right)⋮30\)
`5/2 -3(1/3-x)=1/4-7x`
`=> 5/2 - 1 + 3x=1/4 -7x`
`=>3x+7x= 1/4 - 5/2 +1`
`=> 10x= 1/4 - 10/4 +4/4`
`=>10x= -5/4`
`=>x=-5/4 :10`
`=>x=-5/4 xx1/10`
`=>x= -5/40=-1/8`
\(-23-150+\left(-9\right)+1913\)
\(=1913-\left(23+150+9\right)\)
\(=1913-182\)
\(=1731\)
−23 − 150 + (−9) + 1913
= -23 + (-150) + (-9) + 1913
= -(23 + 150 + 9) + 1913 = -182 + 1913 = 1913 - 182
= 1731
a) (-25)+72-80
=47-80
=-33
b) (-3) . 5 + 28 - (-15)
=-15 +28+15
=(15-15)+28
=0+28
=28
c) (-42) : 7 + (-14) - (-3) . 4
=(-6)-14-(-12)
=-20+12
=-8
d) 15 - 6 : (-3) + (-7) . (-2)
=15-(-2)+14
=17+14
=21
5(x-1)=125-25
5(x-1)=100
x-1=100:5
x-1=20
x=20+1
x=21
12(x-1):3=64+8
12(x-1):3=72
12(x-1)=72.3
12(x-1)=216
x-1=216:12
x-1=18
x=18+1
x=19
(x-1)^3=5^3
=>x-1=5
x=5+1
x=6
\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}\)
\(\text{=}\dfrac{-1}{15}+\dfrac{1}{5}+\dfrac{2}{45}\)
\(\text{=}\dfrac{8}{45}\)
Áp dụng tính chất đổi dấu và giao hoán của phép nhân phân số, ta có:
\(\dfrac{-1}{9}.\dfrac{3}{5}+\dfrac{-1}{4}.\dfrac{-4}{5}+\dfrac{1}{9}.\dfrac{2}{5}=\dfrac{1}{5}.\dfrac{-3}{9}+\dfrac{1}{5}.\dfrac{4}{4}+\dfrac{1}{5}.\dfrac{2}{9}\)
\(=\dfrac{1}{5}\left(-\dfrac{3}{9}+1+\dfrac{2}{9}\right)\)
\(=\dfrac{1}{5}\left(-\dfrac{3}{9}+\dfrac{9}{9}+\dfrac{2}{9}\right)\)
\(=\dfrac{1}{5}.\dfrac{8}{9}\)
\(=\dfrac{8}{45}\)