Giải thích các bước giải:
Ta có:
$A=\dfrac{1}{11}+\dfrac1{12}+\dfrac1{13}+...+\dfrac1{40}$
$\to A=(\dfrac1{11}+\dfrac1{12}+...+\dfrac1{20})+(\dfrac1{21}+\dfrac1{22}+...+\dfrac1{40})$
$\to A>(\dfrac1{20}+\dfrac1{20}+...+\dfrac1{20})+(\dfrac1{40}+\dfrac1{40}+...+\dfrac1{40})$
$\to A>\dfrac12+\dfrac12$
$\to A>1$
Ta có:
$A=\dfrac{1}{11}+\dfrac1{12}+\dfrac1{13}+...+\dfrac1{40}$
$\to A=(\dfrac1{11}+\dfrac1{12}+...+\dfrac1{20})+(\dfrac1{21}+\dfrac1{22}+...+\dfrac1{40})$
$\to A<(\dfrac1{10}+\dfrac1{10}+...+\dfrac1{10})+(\dfrac1{20}+\dfrac1{20}+...+\dfrac1{20})$
$\to A<1+1$
$\to A<2$
Vậy $1<A<2$
