Question

so sánh A và B , biết :A=n/2n+1;B=3n+1/6n+3

Answer 1

\(A=\dfrac{n}{2n+1}=\dfrac{n\left(6n+3\right)}{\left(2n+1\right)\left(6n+3\right)}\dfrac{6n^2+3n}{\left(2n+1\right)\left(6n+3\right)}\)

\(B=\dfrac{3n+1}{6n+3}=\dfrac{\left(3n+1\right)\left(2n+1\right)}{\left(6n+3\right)\left(2n+1\right)}=\dfrac{6n^2+5n+1}{\left(6n+3\right)\left(2n+1\right)}\)

Lại có :

\(6n^2+3n< 6n^2+5n+1\)

\(\Leftrightarrow A< B\)

Answer 2

$A=\frac{n}{2n+1}=\frac{n\left(6n+3\right)}{\left(2n+1\right)\left(6n+3\right)}\frac{6n^2+3n}{\left(2n+1\right)\left(6n+3\right)}$

$B=\frac{3n+1}{6n+3}=\frac{\left(3n+1\right)\left(2n+1\right)}{\left(6n+3\right)\left(2n+1\right)}=\frac{6n^2+5n+1}{\left(6n+3\right)\left(2n+1\right)}$

Lại có :

$6n^2+3n<6n^2+5n+1$

$\iff A<B$