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Số tự nhiên n thỏa mãn:22.32n.\(\left(\frac{2}{3}\right)^n\).2n=82944 là..............(kết quả thôi)
\(2^2.3^{2n}.\left(\frac{2}{3}\right)^n.2^n=82944\)
\(2^2.9^n.\left(\frac{2}{3}\right)^n.2^n=2^{10}.3^4\)
\(2^2.2^n.\left(\frac{2}{3}.9\right)^n=2^{10}.3^4\)
\(2^{n+2}.6^n=2^{10}.3^4\)
\(2^{n+2}.2^n.3^n=2^{10}.3^4\)
\(2^{2n+2}.3^n=2^{10}.3^4\)
Vậy n = 4
\(2^2\cdot3^{2n}\cdot\left(\frac{2}{3}\right)^n\cdot2^n=82944\)
\(2^2\cdot\left(3^2\right)^n\cdot\left(\frac{2^n}{3^n}\right)\cdot2^n=82944\)
\(2^2\cdot9^n\cdot\frac{2^n}{3^n}\cdot2^n=82944\)
\(2^2\cdot\frac{9^n\cdot2^n}{3^n}\cdot2^n=82944\)
\(2^2\cdot\frac{18^n}{3^n}\cdot2^n=82944\)
\(4\cdot6^n\cdot2^n=82944\)
\(6^n\cdot2^n=82944:4\)
\(12^n=20736\)
\(12^n=12^4\)
Vậy n=4
M = 1/3 + (1/3)^2 + ..+ (1/3)^2013
3M = 1 + 1/3+ ...+ (1/3)^2012
3M - M = 1+ 1/3 + (1/3)^2 + ..+ (1/3)^2012 - 1/3 - ...- (1/3)^2013
2M = (1/3 - 1/3) +..+[(1/3)^2012 -(1/3)2012]+ [1 - (1/3)^2013]
2M = 0 + 0 + .. + 0 + 1 - (1/3)^2013
2M = 1 - (1/3)^2013
1 - 2M = 1 - 1 + (1/3)^2013
1 - 2M = (1/3)^2013
(1/3)^2013 = (1/3)^n
2013 = n
Vậy n = 2013
\(\left(\frac{1}{2}\right)^n=\left(\frac{1}{8}\right)^5\)
\(\left(\frac{1}{2}\right)^n=\left(\frac{1^3}{2^3}\right)^5\)
\(\left(\frac{1}{2}\right)^n=\left[\left(\frac{1}{2}\right)^3\right]^5\)
\(\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^{15}\)
n = 15
\(\left(\frac{1}{2}\right)^n=\left(\frac{1}{8}\right)^5\)
\(\Rightarrow\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^{3.5}\)
\(\Rightarrow\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^{15}\)
\(\Rightarrow n=15\)
Vậy n = 15
M = 1/3 + (1/3)^2 + ..+ (1/3)^2013
3M = 1 + 1/3+ ...+ (1/3)^2012
3M - M = 1+ 1/3 + (1/3)^2 + ..+ (1/3)^2012 - 1/3 - ...- (1/3)^2013
2M = (1/3 - 1/3) +..+[(1/3)^2012 -(1/3)2012]+ [1 - (1/3)^2013]
2M = 0 + 0 + .. + 0 + 1 - (1/3)^2013
2M = 1 - (1/3)^2013
1 - 2M = 1 - 1 + (1/3)^2013
1 - 2M = (1/3)^2013
(1/3)^2013 = (1/3)^n
2013 = n
Vậy n = 2013
M = 1/3 + (1/3)^2 + ..+ (1/3)^2013
3M = 1 + 1/3+ ...+ (1/3)^2012
3M - M = 1+ 1/3 + (1/3)^2 + ..+ (1/3)^2012 - 1/3 - ...- (1/3)^2013
2M = (1/3 - 1/3) +..+[(1/3)^2012 -(1/3)2012]+ [1 - (1/3)^2013]
2M = 0 + 0 + .. + 0 + 1 - (1/3)^2013
2M = 1 - (1/3)^2013
1 - 2M = 1 - 1 + (1/3)^2013
1 - 2M = (1/3)^2013
(1/3)^2013 = (1/3)^n
2013 = n
Vậy n = 2013
a) S hình thoi là:
(19 x 12) : 2 = 114(cm2)
b) S hình thoi là;
(30 x 7) : 2 = 105(cm2)
\(2^n.3^{2n}.\left(\frac{2}{3}\right)^n.2^n=82944\)(n\(\in\)N)
\(2^n.2^n.\left(\frac{2}{3}\right)^n.\left(3^2\right)^n=82944\)
\(\left(2.2.\frac{2}{3}.9\right)^n=82944\)
\(24^n=82944\)
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