Câu hỏi của Nguyễn Linh

Question

cho A=1/2*2+1/3*2+...+1/2012*2+1/2013*2

so sánh A với 1

Snow Princess · Accepted Answer

$A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2012^2}+\dfrac{1}{2013^2}$

$A< \dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2012.2013}+\dfrac{1}{2013.2014}$

$A< \dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2012}-\dfrac{1}{2013}+\dfrac{1}{2013}-\dfrac{1}{2014}$

$A< \dfrac{1}{2}-\dfrac{1}{2014}$

$A< \dfrac{1007}{2014}-\dfrac{1}{2014}$

$A< \dfrac{1006}{2014}< 1$

$\Rightarrow A< 1$Câu trả lời: $A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2012^2}+\dfrac{1}{2013^2}$

$A< \dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2012.2013}+\dfrac{1}{2013.2014}$

$A< \dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2012}-\dfrac{1}{2013}+\dfrac{1}{2013}-\dfrac{1}{2014}$

$A< \dfrac{1}{2}-\dfrac{1}{2014}$

$A< \dfrac{1007}{2014}-\dfrac{1}{2014}$

$A< \dfrac{1006}{2014}< 1$

$\Rightarrow A< 1$

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