Đáp án:
Giải thích các bước giải:
Ta thấy: \(\dfrac{1}{3^2}< \dfrac{1}{2.3}\)
\(\dfrac{1}{4^2}< \dfrac{1}{3.4}\)
\(...\)
\(\dfrac{1}{10^2}< \dfrac{1}{9.10}\)
\(\Rightarrow\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{10^2}< \dfrac{1}{2.3}+...+\dfrac{1}{9.10}\)
\(\Rightarrow\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{10^2}< \dfrac{1}{2}-\dfrac{1}{10}\)
\(\Rightarrow\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{100^2}< \dfrac{4}{10}< \dfrac{5}{10}< \dfrac{1}{2}\) (ĐPCM)
