Ta có :
\(A=\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+................+\dfrac{1}{50^2}\)
\(A=1+\dfrac{1}{2^2}+\dfrac{1}{3^2}+.................+\dfrac{1}{50^2}\)
\(\Rightarrow A< 1+\dfrac{1}{1.2}+\dfrac{1}{2.3}+..............+\dfrac{1}{49.50}\)
\(A< 1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.............+\dfrac{1}{49}-\dfrac{1}{50}\)
\(A< 1+1-\dfrac{1}{50}\)
\(A< 2-\dfrac{1}{50}< 2\)
\(\Rightarrow A< 2\rightarrowđpcm\)
~ Chúc bn học tốt ~
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