Câu hỏi của Nìm Hoán Tài

Question

so sánh: 1/4+1/9+1/16+1/25+1/36và5/6

Trúc Giang · Accepted Answer

$A=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}$

$A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}$

⇒ A <  $\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}$

⇒ A < $1-\frac{1}{6}$

Mà $1-\frac{1}{6}$= $\frac{5}{6}$

⇒ A < $\frac{5}{6}$Câu trả lời: $A=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}$

$A=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}$

⇒ A <  $\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}$

⇒ A < $1-\frac{1}{6}$

Mà $1-\frac{1}{6}$= $\frac{5}{6}$

⇒ A < $\frac{5}{6}$

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