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-lt-2M-0-M-2-then-u-n-lt-u-n-1-for-n-1-

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