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(1-1/2) x ( 1-1/3) x (1-1/4) x ..... x (1-1/2011) x (1-1/2012)
= 1/2 x 2/3 x 3/4 x ...... x 2010/2011 x 2011/2012
suy ra loại các nhân tử chung ( ko cần viết phần này )
= 1/2012
chúc học tốt
em mới học lớp 5 có j sai cho em xl
\(\left(5^2\times2^3-7^3\times2\right)\div2\times6-7\div2^5\)
\(=\left(25\times8-343\times2\right)\div2\times6-7\div32\)
\(=\left(200-686\right)\div2\times6-7\div32\)
\(=-486\div2\times6-7\div32\)
\(=-1458-0,21875\)
\(=-1458,21875\)
a)\(x^{15}=x\Rightarrow x\in\left\{0;1\right\}\) d)Là ý b
b)\(\left(2x+1\right)^3=125\\ \left(2x+1\right)^3=5^3\Rightarrow2x+1=5\\ 2x=4\\ x=2\) e)\(\left(x-3\right)^2=25\\ \Rightarrow\left(x-3\right)^2=5^2\\ \Rightarrow\hept{\begin{cases}x-3=5\Rightarrow x=8\\x-3=-5\Rightarrow x=-2\end{cases}}\)
c)\(\left(x-5\right)^4=\left(x-5\right)^6\\ \Rightarrow x-5\in\left\{0;1\right\}\Rightarrow x\in\left\{5;6\right\}\)
\(\left(5.2^2-20\right):\left(5+3^2:6\right)\\ =\left(5.4-20\right):\left(5+9:6\right)\\ =\left(20-20\right):\left(5+\dfrac{3}{2}\right)\\ =1:\dfrac{13}{2}=\dfrac{2}{13}\)
707: [(2x -5) + 74] = 42 - 32
(2x -5) + 74 = 101
2x - 5 + 74 = 101
2x + 69 = 101
2x = 32 = 25
=> x = 5
707: [(2x -5) + 74] = 42 - 32
(2x -5) + 74 = 101
2x - 5 + 74 = 101
2x + 69 = 101
2x = 32 = 25
=> x = 5
\(36\cdot4-4\cdot\left[82-7\cdot11\right]^2:4-2016^0\)
=9-1-5^2
=8-25=-17
Đặt \(C=\dfrac{3}{2}+\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+...+\left(\dfrac{3}{2}\right)^{2012}\)
=>\(\dfrac{3}{2}C=\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+...+\left(\dfrac{3}{2}\right)^{2013}\)
=>\(\dfrac{3}{2}C-C=\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+...+\left(\dfrac{3}{2}\right)^{2013}-\dfrac{3}{2}-\left(\dfrac{3}{2}\right)^2-...-\left(\dfrac{3}{2}\right)^{2012}\)
=>\(\dfrac{1}{2}C=\left(\dfrac{3}{2}\right)^{2013}-\dfrac{3}{2}\)
=>\(\dfrac{C}{2}=\dfrac{3^{2013}-3\cdot2^{2012}}{2^{2013}}\)
=>\(C=\dfrac{3^{2013}-3\cdot2^{2012}}{2^{2012}}\)
=>\(A=\dfrac{1}{2}+C=\dfrac{1}{2}+\dfrac{3^{2013}-3\cdot2^{2012}}{2^{2012}}=\dfrac{2^{2011}+3^{2013}-3\cdot2^{2012}}{2^{2012}}\)
=>\(A=\dfrac{3^{2013}+2^{2011}\left(1-3\cdot2\right)}{2^{2012}}=\dfrac{3^{2013}-5\cdot2^{2011}}{2^{2012}}\)
\(B-A=\left(\dfrac{3}{2}\right)^{2013}:2-\dfrac{3^{2013}-5\cdot2^{2011}}{2^{2012}}=\dfrac{3^{2013}}{2^{2014}}-\dfrac{3^{2013}-5\cdot2^{2011}}{2^{2012}}\)
\(=\dfrac{3^{2013}-4\cdot3^{2013}+20\cdot2^{2011}}{2^{2014}}=\dfrac{-3^{2014}+5\cdot2^{2013}}{2^{2014}}\)
sao đóng ngoặc mà ko có mở vậy