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Question Number 194526 by mathlove last updated on 09/Jul/23

$$\frac{f(x+1)}{f\left(x\right)}=x^{2}f\left(x\right)=?$$$$\frac{f\left(6\right)}{f\left(3\right)}=?$$

Answered by JDamian last updated on 09/Jul/23

$$\frac{f\left(6\right)}{f\left(3\right)}=\frac{f\left(6\right)}{f\left(3\right)}\times \frac{f\left(5\right)}{f\left(5\right)}\times \frac{f\left(4\right)}{f\left(4\right)}=$$$$=\frac{f\left(6\right)}{f\left(5\right)}\times \frac{f\left(5\right)}{f\left(4\right)}\times \frac{f\left(4\right)}{f\left(3\right)}=5^2\times 4^2\times 3^2=3600$$

Answered by MM42 last updated on 09/Jul/23

$$ifx\in \mathbb{N}\Rightarrow f(n+1)=n^{2}f\left(n\right)=n^2\times {(n-1)}^{2}f(n-1)$$$$=...={(n!)}^2\times f\left(1\right)$$

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