3⁴ . 71 - 3⁴ . 2⁹ 

3⁴ . ( 71 - 2⁹ )

3⁴ . -441 

= -35721

(3³ . 5² - 2⁴ - 16 ) . 13 

= ( 27 . 25- 16 - 16 ) . 13 

= ( 675 - 16 -16 ) . 13 

=  643. 13 

= 8359

35.237 +33.35 

=35 . ( \(237+33\) ) 

= 35 . 270 

= 9450 

  2³ . 4² + 2³ . 84 - 40 

=2³ . ( 16 + 84 ) - 40 

= 8 . 100 - 40 

= 800 - 40 

= 760 

\(=\dfrac{1}{3}-\dfrac{1}{2}\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{33\cdot35}\right)\)

\(=\dfrac{1}{3}-\dfrac{1}{2}\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{33}-\dfrac{1}{35}\right)\)

\(=\dfrac{1}{3}-\dfrac{1}{2}\cdot\dfrac{32}{105}=\dfrac{19}{105}\)

đặt A=6/5.7+6/7.9+6/9.11+......+6/33.35

\(\Leftrightarrow A=3\left(\frac{2}{5\cdot7}+\frac{6}{7\cdot9}+...+\frac{6}{33\cdot35}\right)\)

\(\Rightarrow A=3\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{33}-\frac{1}{35}\right)\)

\(\Rightarrow A=3\left(\frac{1}{5}-\frac{1}{35}\right)\)

\(\Rightarrow A=3\cdot\frac{6}{35}\)

\(\Rightarrow A=\frac{18}{35}\)

đặt A=6/5.7+6/7.9+6/9.11+......+6/33.35

\(\Leftrightarrow A=3\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{33\cdot35}\right)\)

\(\Rightarrow A=3\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{33}-\frac{1}{35}\right)\)

\(\Rightarrow A=3\left(\frac{1}{5}-\frac{1}{35}\right)\)

\(\Rightarrow A=3\cdot\frac{6}{35}\)

\(\Rightarrow A=\frac{18}{35}\)

Gọi A là biểu thức \(\frac{6}{5\cdot7}+\frac{6}{7\cdot9}+...+\frac{6}{33\cdot35}\)

Ta có: \(\frac{6}{5\cdot7}+\frac{6}{7\cdot9}+...+\frac{6}{33\cdot35}\)

\(\Rightarrow A=3\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{33}-\frac{1}{35}\right)\)

\(\Rightarrow A=3\left(\frac{1}{5}-\frac{1}{35}\right)=3\cdot\frac{6}{35}=\frac{18}{35}\)

a: \(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdots+\frac{1}{49\cdot50}\)

\(=1-\frac12+\frac12-\frac13+\cdots+\frac{1}{49}-\frac{1}{50}\)

\(=1-\frac{1}{50}=\frac{49}{50}\)

b: \(B=-\frac13-\frac{1}{15}-\cdots-\frac{1}{33\cdot35}\)

\(=-\frac12\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\cdots+\frac{2}{33\cdot35}\right)\)

\(=-\frac12\left(1-\frac13+\frac13-\frac15+\cdots+\frac{1}{33}-\frac{1}{35}\right)\)

\(=-\frac12\left(1-\frac{1}{35}\right)=-\frac12\cdot\frac{34}{35}=-\frac{17}{35}\)

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