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compare 2 fractions with 2022 fractions each

Source: 2022 South Russian Girls MO - Assara Juniors p7

February 28, 2024
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Problem Statement

Find out which of the two numbers is greater: 22+22+2...+22+22   or   33+33+3...+33+33\dfrac{2}{2 +\dfrac{2}{2 +\dfrac{2}{... +\dfrac{2}{2+\frac22}}}} \,\,\, \text{or} \,\,\, \dfrac{3}{3 +\dfrac{3}{3 +\dfrac{3}{... +\dfrac{3}{3+\frac33}}}} (Each expression has 20222022 fraction signs.)
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