>

=

>

<

3/2  ..>.   2/3

15/6 .=.. 5/2

4/3 ..>. 5/7

8/9 .<.. 1

>

=

>

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Trả lời

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Câu hỏi của 123456 - Toán lớp 6 - Học toán với OnlineMath

~Hok tốt~

Vì 3^10+1/3^9+1>1 =>3^10+1/3^9+1>3^10+1+2/3^10+1+2 =3.(3^9+1)/3.(3^8+1)

                                                                                               =3^9+1/3^8+1

=>3^10+1/3^9+1 > 3^9+1/3^8+1

Vậy 3^10+1/3^19+1 > 3^9+1/3^8+1

Ta có: \(A=\dfrac{3^{10}+1}{3^9+1}\)

\(\Leftrightarrow A=\dfrac{3^{10}+3-2}{3^9+1}\)

hay \(A=3-\dfrac{2}{3^9+1}\)

Ta có: \(B=\dfrac{3^9+1}{3^8+1}\)

\(\Leftrightarrow B=\dfrac{3^9+3-2}{3^8+1}\)

hay \(B=3-\dfrac{2}{3^8+1}\)

Ta có: \(3^9+1>3^8+1\)

\(\Leftrightarrow\dfrac{2}{3^9+1}< \dfrac{2}{3^8+1}\)

\(\Leftrightarrow-\dfrac{2}{3^9+1}>-\dfrac{2}{3^8+1}\)

\(\Leftrightarrow-\dfrac{2}{3^9+1}+3>-\dfrac{2}{3^8+1}+3\)

hay A>B

Có : A = 3.(3^9+1)-2/3^9+1 = 3 - 2/3^9+1

B = 3.(3^8+1)-2/3^8+1 = 3 - 2/3^8+1

Vì 3^9+1 > 3^8+1 => 2/3^9+1 < 2/3^8+1

=> -2/3^9+1 > -2/3^8+1

=> A > B

Tk mk nha

A=3.(3⁹+1)-2

A= 1/3+1/6+1/10+...+1/561

  = 2. (1/6+1/12+1/20+...+1/1122)

  = 2. [1/(2.3) + 1/(3.4) + 1/(4.5) +...+1/(33.34)]

  = 2. ( 1/2 - 1/3 +1/3 - 1/4 + 1/4 - 1/5 +...+ 1/33 - 1/34 )

  =2. (1/2 - 1/34)

  =2. 8/17

  =16/17

Vì 16/17 > 16/18 = 8/9 -> A > 8/9