5/7 x 6/11 + 5/11 x 1/7 - 5/7 x 14/11
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\(\dfrac{5}{7}\cdot\dfrac{6}{11}+\dfrac{5}{11}\cdot\dfrac{1}{7}-\dfrac{5}{7}\cdot\dfrac{14}{11}\)
\(=\dfrac{5}{7}\cdot\dfrac{6}{11}+\dfrac{5}{7}\cdot\dfrac{1}{11}-\dfrac{5}{7}\cdot\dfrac{14}{11}\)
\(=\dfrac{5}{7}\cdot\left(\dfrac{6}{11}+\dfrac{1}{11}-\dfrac{14}{11}\right)\)
\(=\dfrac{5}{7}\cdot\dfrac{-7}{11}=\dfrac{-5}{11}\)
3\(^{x+1}\) - 3\(^x\) = 1428
3\(^x\).( 3 - 1) = 1428
3\(^x\).2 = 1428
3\(^x\) = 1428: 2
3\(^x\) = 714
3\(^{x+1}\) là số lẻ \(\forall\) \(x\) ⇒ 3\(^x\) \(\ne\) 714 ∀ \(x\) ⇒ \(x\) \(\in\) \(\varnothing\)
`#3107`
\(\left(2x-\dfrac{1}{2}\right)^2+\dfrac{3}{7}=\dfrac{19}{8}\\ \Rightarrow\left(2x-\dfrac{1}{2}\right)^2=\dfrac{19}{8}-\dfrac{3}{7}\\ \Rightarrow\left(2x-\dfrac{1}{2}\right)^2=\dfrac{109}{56}\\ \Rightarrow\left(2x-\dfrac{1}{2}\right)^2=\left(\sqrt{\dfrac{109}{56}}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}2x-\dfrac{1}{2}=\sqrt{\dfrac{109}{56}}\\2x-\dfrac{1}{2}=-\sqrt{\dfrac{109}{56}}\end{matrix}\right.\)
Bạn xem lại đề, số lớn quá ;-;.
B = \(\dfrac{1}{2^3}\) + \(\dfrac{2}{3^3}\) + \(\dfrac{3}{4^3}\)+...+ \(\dfrac{n-1}{n^3}\) (n > 2)
Vì n > 2 ⇒ B > 0 (1)
\(\dfrac{1}{2^3}\) < \(\dfrac{1}{2^2}\) < \(\dfrac{1}{1.2}\) = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\)
\(\dfrac{2}{3^3}\) < \(\dfrac{3}{3^3}\) = \(\dfrac{1}{3^2}\) < \(\dfrac{1}{2.3}\) = \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\)
\(\dfrac{3}{4^3}\) < \(\dfrac{4}{4^3}\) = \(\dfrac{1}{4^2}\) < \(\dfrac{1}{3.4}\) = \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\)
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\(\dfrac{n-1}{n^3}\)<\(\dfrac{n^{ }}{n^3}\) = \(\dfrac{1}{n^2}\) < \(\dfrac{1}{\left(n-1\right).n}\) = \(\dfrac{1}{n-1}\) - \(\dfrac{1}{n}\)
Cộng vế với vế ta có:
B < 1 - \(\dfrac{1}{n}\) < 1 (2)
Kết hợp (1) và(2) ta có: 0 < B < 1
Vậy B không phải là số tự nhiên (đpcm)
`#3107.101107`
\(\dfrac{5}{7}\times\dfrac{6}{11}+\dfrac{5}{11}\times\dfrac{1}{7}-\dfrac{5}{7}\times\dfrac{14}{11}\\ =\dfrac{5}{7}\times\dfrac{6}{11}+\dfrac{5}{7}\times\dfrac{1}{11}-\dfrac{5}{7}\times\dfrac{14}{11}\\ =\dfrac{5}{7}\times\left(\dfrac{6}{11}+\dfrac{1}{11}-\dfrac{14}{11}\right)\\ =\dfrac{5}{7}\times\left(-\dfrac{7}{11}\right)\\ =-\dfrac{5}{11}\)