Proving ${\psi}_{n}(x)\le F(n)$ by Induction

[sarrah1]

Hello

is my proof be correct ?

I wish to prove by induction that ${\psi}_{n}(x)\le F(n)$ , $x\in[a,b]$ ... (1)

Let there exists a function $f(x,n)$ such that if ${\psi}_{n}(x)\le f(x,n) $ then ${\psi}_{n}(x) \le F(n)$ .

I know that (1) is true for $n=1$ i.e. ${\psi}_{1}(x)\le f(x,1)\le F(1)$ ,

and I was able to prove that

${\psi}_{n+1}(x)\le F(n+1)$ , $x\in[a,b]$

would this implies ${\psi}_{n}(x)\le F(n)$

thanks

 

[Evgeny.Makarov]

I wish to prove by induction that ${\psi}_{n}(x)\le F(n)$ , $x\in[a,b]$

Please provide the definitions of $\psi_n$, $F$, $a$ and $b$.