1-prove-that-x-0-1-1-1-x-lnx-x-1-2-find-2-sequences-u-n-and-v-n-u-n-k-1-n-1-ln-k-n-v-n-n-2-

Question Number 34258 by math khazana by abdo last updated on 03/May/18

1) p r o v e t h a t \forall x \in] 0, 1 [1 - \frac{1}{x} ⩽ l n x ⩽ x - 1

2) f i n d 2 s e q u e n c e s u_{n} a n d v_{n} /

u_{n} ⩽ \prod_{k = 1}^{n - 1} l n (\frac{k}{n}) ⩽ v_{n} \forall n ⩾ 2

Commented by math khazana by abdo last updated on 03/May/18

2) t h e Q i s e^{u_{n}} ⩽ \prod_{k = 1}^{n} \frac{k}{n} ⩽ e^{v_{n}} \forall n ⩾ 2