The actual question is prove that [tex] |\alpha|!\le n^{|\alpha|}\alpha![/tex] where(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\alpha=(\alpha_1,.....\alpha_n)[/tex] is a multi-index (all non-negative) and [tex]

|\alpha|=\alpha_1+\cdots +\alpha_n [/tex] and [tex]\alpha!=\alpha_1!\cdots \alpha_n! [/tex] so I am trying to do it by induction on the number of elements [tex]n[/tex] in [tex]\alpha[/tex]...so I am trying to prove that [tex](a+b)!<2^{a+b}a!b! [/tex] I have tried to do this by induction on the value of b (the inequality is obvious for b=0 or 1), and other ways, but nothing is working (been trying for close to a week).

Can someone please help? :)

(ps. how do I make it so that after I write in latex it doesn't skip a line like that?)

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# Prove (a+b)!<a!b!2^(a+b) help please!

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