Question

giả hộ mình với

Answer 1

\(\sqrt{1903\sqrt{1904\sqrt{1905\sqrt{...\sqrt{2501}}}}}\\ < \sqrt{1903\sqrt{1904\sqrt{1905\sqrt{2500\cdot2502}}}}\)

\(=\sqrt{1903\sqrt{1904\sqrt{1905...\sqrt{2499\left(2501^2-1\right)}}}}\)

\(< \sqrt{1903\sqrt{1904\sqrt{1905...\sqrt{2499\cdot2501}}}}\)

\(=\sqrt{1903\sqrt{1904\sqrt{1905\sqrt{2498\left(2500^2-1\right)}}}}\)

\(< \sqrt{1903\sqrt{1904\sqrt{1905...\sqrt{2498\cdot2500}}}}\)

\(< ...< \sqrt{1903\cdot1905}< 1904\)