Bài 1 :
\(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+............+\dfrac{1}{7^2}\)
Ta thấy :
\(\dfrac{1}{2^2}< \dfrac{1}{1.2}\)
\(\dfrac{1}{3^2}< \dfrac{1}{2.3}\)
..................
\(\dfrac{1}{7^2}< \dfrac{1}{6.7}\)
\(\Leftrightarrow A< \dfrac{1}{1.2}+\dfrac{1}{2.3}+.....+\dfrac{1}{6.7}\)
\(\Leftrightarrow A< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+........+\dfrac{1}{6}-\dfrac{1}{7}\)
\(\Leftrightarrow A< 1-\dfrac{1}{7}< 1\)
\(\Leftrightarrow A< 1\rightarrowđpcm\)
Câu 2 có vấn đề nặng nề :v
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