Can we simplify this expression?
$$A_n=\frac{\prod\limits^n_{k=0}((2k+1)^4+\dfrac{1}{4})}{\prod\limits^{n+1}_{k=1}((2k)^4+\dfrac{1}{4})}$$
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Try to write this down for some easy numbers (like from 3 to 6) and see what happens. – Dominique Sep 22 '23 at 11:19
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@Dominique explain your idea – deval sidi Sep 22 '23 at 12:00
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Note that $k^4+\frac14=\left(k^2-k+\frac12\right)\left(k^2+k+\frac12\right).$ Use Approach0. – PinkyWay Sep 22 '23 at 12:43
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1@Invisible thank you very much sir and merci beaucoup – deval sidi Sep 22 '23 at 15:13
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De rien, Deval! (=: – PinkyWay Sep 22 '23 at 17:29