2tính nhanh
1x3x9+2x6x18+3x9x27phần
1x5x18+2x10x36+3x15x54
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\(\left(3x-2\right)^2-2\left(x-1\right)^2\)
\(=9x^2-18x+4-2\left(x^2-2x+1\right)\)
\(=9x^2-18x+4-2x^2+4x-2\)
\(=7x^2-14x+2\)
\(\left(3x-2\right)^2-2\left(x-1\right)^2=9x^2-12x+4-2x^2+4x-2=7x^2-8x+2\)
Đặt N = 1 + 2 + 22 +...+ 22012
2N = 2 + 22 + 23 +...+ 22013
2N - N = (2 + 22 + 23+....+ 22013) - (1 + 2 + 22 +....+ 22012)
N = 22013 - 1
Thay N vào M ta được:
\(M=\dfrac{2^{2013}-1}{2^{2014}-2}=\dfrac{2^{2013}-1}{2\left(2^{2013}-1\right)}=\dfrac{1}{2}\)Đặt \(N=1+2+2^2+...+2^{2012}\)
\(2N=2+2^2+2^3+...+2^{2013}\)
\(2N-N=\left(2+2^2+2^3+...+2^{2013}\right)-\left(1+2+2^2+...+2^{2012}\right)\)
\(N=2^{2013}-1\)
Thay N vào M ta được:
\(M=\dfrac{2^{2013-1}}{2^{2014}-2}=\dfrac{2^{2013}-1}{2\left(2^{2013}-1\right)}=\dfrac{1}{2}\)
Sửa đề: \(M=\frac{1+2+2^2+\cdots+2^{2012}}{2^{2014}-2}\)
Đặt \(A=1+2+2^2+\cdots+2^{2012}\)
=>\(2A=2+2^2+2^3+\cdots+2^{2013}\)
=>2A-A=\(2+2^2+2^3+\cdots+2^{2013}-1-2-2^2-\cdots-2^{2012}\)
=>\(A=2^{2013}-1\)
Ta có: \(M=\frac{1+2+2^2+\cdots+2^{2012}}{2^{2014}-2}\)
\(=\frac{2^{2013}-1}{2\left(2^{2013}-1\right)}=\frac12\)
\(\left(3x-2\right)^2-2\left(x-1\right)^2\)
\(=9x^2-12x+4-2\left(x^2-2x+1\right)\)
\(=9x^2-12x+4-2x^2+4x-2\)
\(=7x^2-16x+2\)
\(f\left(-2\right)=12\cdot\left(-8\right)-14\cdot4+2=-96+2-56=-160\)
\(\frac{1\times3\times9+2\times6\times18+3\times9\times27}{1\times5\times18+2\times10\times36+3\times15\times54}\)
\(=\frac{1\times3\times9\times\left(1+2\times2\times2+3\times3\times3\right)}{1\times5\times18\times\left(1+2\times2\times2+3\times3\times3\right)}\)
\(=\frac{3\times9}{5\times18}=\frac{27}{90}=\frac{3}{10}\)