Lời giải:
$A=\dfrac{2^2}{3.5}+\dfrac{2^2}{5.7}+\dfrac{2^2}{7.9}+...+\dfrac{2^2}{69.71}$
$A=2(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{69.71})$
$A=2(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{69}-\dfrac{1}{71})$
$A=2(\dfrac{1}{3}-\dfrac{1}{71})$
$A=2.\dfrac{68}{213}$
$A=\dfrac{136}{213}$
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2)
Đặt d là UC{ 14n+3 ; 21n+5}
14n+3 chia hết cho d.
21n+5 chia hết cho d.
$\left \{ {{42n+10} \atop {42n+9}} \right.$
`=> 1 ⋮ d`
`=>d=1`
Vậy phân số A tối giản.
