Question

So sánh 10^n/ 10^n+1 và 10^n+1/ 10^n+2

Answer 1

Giải:

Ta có:

\(\dfrac{10^n}{10^n+1}=\dfrac{10^n+1-1}{10^n+1}=1-\dfrac{1}{10^n+1}\)

\(\dfrac{10^n+1}{10^n+2}=\dfrac{10^n+2-1}{10^n+2}=1-\dfrac{1}{10^n+2}\)

Vì \(\dfrac{1}{10^n+1}>\dfrac{1}{10^n+2}\)

\(\Leftrightarrow-\dfrac{1}{10^n+1}< -\dfrac{1}{10^n+2}\)

\(\Leftrightarrow-\dfrac{1}{10^n+1}+1< -\dfrac{1}{10^n+2}+1\)

Hay \(1-\dfrac{1}{10^n+1}< 1-\dfrac{1}{10^n+2}\)

\(\Leftrightarrow\dfrac{10^n}{10^n+1}< \dfrac{10^n+1}{10^n+2}\)

Vậy ...