Question

So sánh-+

 \(\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+...+\sqrt{4}}}}}\) và \(3\)

Answer 1

100 dấu căn nha

Answer 2

\(\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+...}}}}< \sqrt{6+\sqrt{6+\sqrt{6+...\sqrt{6+\sqrt{9}}}}}\)(100 dấu căn)

=> \(VT< \sqrt{6+\sqrt{6+\sqrt{6+...\sqrt{6+3}}}}=\sqrt{6+\sqrt{6+\sqrt{6+..\sqrt{6+\sqrt{9}}}}}\)(99 dấu căn)

=> \(VT< \sqrt{6+3}=3\)