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Part of 1992 Tournament Of Towns

Problems(1)

TOT 326 1992 Spring A J3 compare nested radicals

Source:

6/9/2024
Let n,m,kn, m, k be natural numbers, with m>nm > n. Which of the numbers is greater: n+m+n+...   or    m+n+m+...  ?\sqrt{n+\sqrt{m+\sqrt{n+...}}}\,\,\, or \,\,\,\, \sqrt{m+\sqrt{n+\sqrt{m+...}}}\,\, ? Note: Each of the expressions contains kk square root signs; n,mn, m alternate within each expression.
(N. Kurlandchik)
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