\(A=2\sqrt{1}+2\sqrt{3}+...+2\sqrt{21}\)
\(A=2.\left(\sqrt{1}+\sqrt{3}+...+\sqrt{21}\right)\)
\(B=2\sqrt{2}+2\sqrt{4}+....2\sqrt{22}\)
\(B=2.\left(\sqrt{2}+\sqrt{4}+...+\sqrt{22}\right)\)
Có \(\sqrt{1}+\sqrt{3}+...+\sqrt{21}\) Có 11 số hạng.
\(\sqrt{2}+\sqrt{4}+...+\sqrt{22}\) Có 11 số hạng.
Mà \(\hept{\begin{cases}\sqrt{1}< \sqrt{2}\\....\\\sqrt{21}< \sqrt{22}\end{cases}}\)
=> \(2.\left(\sqrt{1}+\sqrt{3}+...+\sqrt{21}\right)< 2.\left(\sqrt{2}+\sqrt{4}+...+\sqrt{22}\right)\)
\(\Rightarrow A< B\)