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TOT 326 1992 Spring A J3 compare nested radicals

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June 9, 2024
algebrainequalitiesCompareradical

Problem Statement

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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