Question

So sánh : A=1/20^2+1/21^2+1/22^2+...+1/30^2 và B=1/19

 

Answer 1

Ta có:

\(\dfrac{1}{20^2}< \dfrac{1}{20\cdot19}=\dfrac{1}{19}-\dfrac{1}{20}\)

\(\dfrac{1}{21^2}< \dfrac{1}{20\cdot21}=\dfrac{1}{20}-\dfrac{1}{21}\)

\(...\)

\(\dfrac{1}{30^2}< \dfrac{1}{29\cdot30}=\dfrac{1}{29}-\dfrac{1}{30}\)

\(\Rightarrow A< \dfrac{1}{19}-\dfrac{1}{30}< \dfrac{1}{19}\)