Đáp án: 2.$x=16$
Giải thích các bước giải:
1.Ta có :
$A=\dfrac{3^2}{20.23}+\dfrac{3^2}{23.26}+...+\dfrac{3^2}{77.80}$
$\to A=3(\dfrac{3}{20.23}+\dfrac{3}{23.26}+...+\dfrac{3}{77.80})$
$\to A=3(\dfrac{23-20}{20.23}+\dfrac{26-23}{23.26}+...+\dfrac{80-77}{77.80})$
$\to A=3(\dfrac1{20}-\dfrac1{23}+\dfrac1{23}-\dfrac1{26}+...+\dfrac1{77}-\dfrac1{80})$
$\to A=3(\dfrac1{20}-\dfrac{1}{80})$
$\to A<3\cdot\dfrac1{20}$
$\to A<3\cdot\dfrac13$
$\to A<1$
2.Ta có :
$\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{x(x+2)}=\dfrac49$
$\to\dfrac{4-2}{2.4}+\dfrac{6-4}{4.6}+...+\dfrac{x+2-x}{x(x+2)}=\dfrac49$
$\to \dfrac12-\dfrac14+\dfrac14-\dfrac16+...+\dfrac1{x}-\dfrac{1}{x+2}=\dfrac49$
$\to\dfrac12-\dfrac1{x+2}=\dfrac49$
$\to \dfrac1{x+2}=\dfrac12-\dfrac49$
$\to\dfrac1{x+2}=\dfrac1{18}$
$\to x+2=18$
$\to x=16$
