Question

Cho S= 1/11+ 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20
So sánh S với 1/2
Mn giúp mình với

Answer 1

-Ta có: \(\dfrac{1}{2}=\dfrac{10}{20}=\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}\) (có 10 số \(\dfrac{1}{20}\)).

Mà \(\dfrac{1}{20}< \dfrac{1}{19};\dfrac{1}{20}< \dfrac{1}{18};...;\dfrac{1}{20}< \dfrac{1}{11}\)

\(\Rightarrow\dfrac{1}{20}+\dfrac{1}{20}+...+\dfrac{1}{20}< \dfrac{1}{20}+\dfrac{1}{19}+\dfrac{1}{18}+...+\dfrac{1}{11}\)

\(\Rightarrow\dfrac{1}{2}< S\)