Let f∈C^∞ (R,R) , ∀ n∈N M_n =∣∣f^((n)) ∣∣_∞ and u_n =((2^(n−1) M_n )/M_(n−1) ) for n≥1 Show that if M_1 <(√(2M_0 M_2 )) then u_n <u


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Question Number 127631 by snipers237 last updated on 31/Dec/20

$L e t f \in C^{\infty} (R, R), \forall n \in N M_{n} =∣∣ f^{(n)} ∣ ∣_{\infty}$ $a n d u_{n} = \frac{2^{n - 1} M_{n}}{M_{n - 1}} f o r n ⩾ 1$ $S h o w t h a t i f M_{1} < \sqrt{2 M_{0} M_{2}} t h e n u_{n} < u_{n + 1} f o r n ⩾ 1$
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