Câu hỏi của 🎇 Kamyaki Miyuki 🎇

Question

So sánh

1/2^2 + 1/3^2 +14^2 + .......+1/10^2 với 1

🎇 Kamyaki Miyuki 🎇 · Accepted Answer

Cho mình sửa:

1/2^2 + 1/3^2 +14^2 + .......+1/10^2 với 1 => 1/2^2 + 1/3^2 +1/4^2 + .......+1/10^2 với 1

Câu trả lời:

Cho mình sửa:

1/2^2 + 1/3^2 +14^2 + .......+1/10^2 với 1 => 1/2^2 + 1/3^2 +1/4^2 + .......+1/10^2 với 1

KAl(SO4)2·12H2O · Answer

$\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+...+\frac{1}{9}+\frac{1}{10}$

$=1-\frac{1}{10}< 1$

$\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< 1$

Câu trả lời:

$\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+...+\frac{1}{9}+\frac{1}{10}$

$=1-\frac{1}{10}< 1$

$\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{10^2}< 1$