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\(\dfrac{3}{4}+\dfrac{5}{36}+\dfrac{7}{144}+...+\dfrac{2n+1}{n^2\left(n+1\right)^2}\)
\(=1-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+\dfrac{1}{3^2}-\dfrac{1}{4^2}+...+\dfrac{1}{\left(n-1\right)^2}+\dfrac{1}{n^2}\)
\(=1-\dfrac{1}{n^2}< 1\)
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FC Alan Walker 21/02/2018 at 17:38Ta có: \(\dfrac{2n+1}{n^2\left(n+1\right)^2}=\dfrac{\left(n+1\right)^2-n^2}{n^2\left(n+1\right)^2}=\dfrac{1}{n^2}-\dfrac{1}{\left(n+1\right)^2}\)
Do đó \(\dfrac{3}{4}+\dfrac{5}{36}+\dfrac{7}{144}+...+\dfrac{2n+1}{n^2\left(n+1\right)^2}\)
\(=1-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+\dfrac{1}{3^2}-\dfrac{1}{4^2}+...+\dfrac{1}{n^2}-\dfrac{1}{\left(n+1\right)^2}\)
\(=1-\dfrac{1}{\left(n+1\right)^2}< 1\)
Vậy \(\dfrac{3}{4}+\dfrac{5}{36}+\dfrac{7}{144}+...+\dfrac{2n+1}{n^2\left(n+1\right)^2}< 1\forall n\in\)N*
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sssssssssssssss 01/08/2018 at 07:17c. "My BINGO is a vertical line."
Nobita - Kun selected this answer. -
Nobita - Kun 01/08/2018 at 07:08a. "My BINGO has all prime numbers."
b. "The numbers in my BINGO add up to 138."
c. "My BINGO is a vertical line."
d. "My BINGO uses the FREE space."
Help me this posts
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Vũ Mạnh Hùng 03/02/2018 at 18:49knjip
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FA FIFA Club World Cup 2018 16/01/2018 at 21:54
We have : \(\dfrac{x^2-5x}{x-5}=5\)
\(\dfrac{x\left(x-5\right)}{x-5}=5\)
\(x=5\)
So the experiment of the above equation is \(S=\left\{5\right\}\)
HỦY DIỆT THE WORLD selected this answer. -
Fc Alan Walker 22/01/2018 at 12:28We have : x2−5xx−5=5
x(x−5)x−5=5
x=5
So the experiment of the above equation is S={5}
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FC Alan Walker 21/02/2018 at 17:52
Condition: \(x\ne5\)
We have: \(\dfrac{x^2-5x}{x-5}=5\Leftrightarrow\dfrac{x\left(x-5\right)}{x-5}=5\Leftrightarrow x=5\)
So the experiment of the above equation is \(S=\left\{\phi\right\}\)
Thao Dola
13/03/2017 at 13:30
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Nguyen Thi Thuy Linh 11/04/2017 at 15:15
a)\(2\dfrac{1}{5}+3\dfrac{4}{5}+9\dfrac{6}{5}=\dfrac{11}{5}+\dfrac{19}{5}+\dfrac{51}{5}=\dfrac{11+19+51}{5}=\dfrac{81}{5}\)
b)\(5\dfrac{7}{9}\cdot6\dfrac{2}{4}\cdot4\dfrac{5}{8}=\dfrac{52}{9}\cdot\dfrac{26}{4}\cdot\dfrac{37}{8}=\dfrac{52\cdot26\cdot37}{9\cdot4\cdot8}=\dfrac{50024}{288}=173\dfrac{25}{36}\)
Nguyen Thi Bich Huong selected this answer.
