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3

Part of 1984 Dutch Mathematical Olympiad

Problems(1)

a_n =\frac{1 x 4 x7 x ... (3n-2)}{2 x 5 x 8 x ... (3n-1)

Source: Netherlands - Dutch MO 1984 p3

12/25/2022
For n=1,2,3,...n = 1,2,3,.... ana_n is defined by: an=1⋅4⋅7⋅...(3n−2)2⋅5⋅8⋅...(3n−1)a_n =\frac{1 \cdot 4 \cdot 7 \cdot ... (3n-2)}{2 \cdot 5 \cdot 8 \cdot ... (3n-1)} Prove that for every nn holds that 13n+1≤an≤13n+13\frac{1}{\sqrt{3n+1}}\le a_n \le \frac{1}{\sqrt[3]{3n+1}}
algebrainequalitiesSequence