( 3x - 1,5 )( -1/2x + 5 ) = 0

<=> 3x - 1,5 = 0 hoặc -1/2x + 5 = 0

<=> x = 1/2 hoặc x = 10

Vậy ...

\(\left(3x-1,5\right)\left(-\frac{1}{2}x+5\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}3x-1,5=0\\-\frac{1}{2}x+5=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=10\end{cases}}}\)

Vậy x=1/2 và x=10

Đặt A=1/3²+1/4²+1/5²+...+1/60²
Do 1/3²<1/3.4;1/4²<1/4.5;1/5²<1/5.6;...;1/60²<1/60.61
=>A<1/3.4+1/4.5+1/5.6+...+1/60.61
=>A<1/3-1/4+1/4-1/5+1/5-1/6+...+1/60-1/61
=>A<1/3-1/4
=>A<7/12<4/9
Vậy A<4/9

Đặt tổng trên là A

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2013}}\)

\(A=2A-A=1-\frac{1}{2^{2014}}< 1\)

Đặt tổng trên là A

\(4A=\frac{5-1}{1.5}+\frac{9-5}{5.9}+\frac{13-9}{9.13}+...+\frac{25-21}{21.25}\)

\(4A=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}\)

\(4A=1-\frac{1}{25}\Rightarrow A=\frac{1}{4}-\frac{1}{100}< \frac{1}{4}\)

\(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{21.25}=\frac{1}{4}\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{21.25}\right)\)

\(=\frac{1}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}\right)\)

\(=\frac{1}{4}\left(1-\frac{1}{25}\right)=\frac{1}{4}.\frac{24}{25}=\frac{6}{25}< \frac{1}{4}\)

????cai j v

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