u-n-1-u-n-u-n-3-u-0-0-1-show-that-u-n-0-1-show-that-u-n-converges-to-0-v-n-1-u-n-1-2-1-u-n-2-express-v-n-interms-of-u-n-show-that-v-n-converges-to-2-f-

Question Number 208418 by alcohol last updated on 16/Jun/24

u_{n + 1} = u_{n} - u_{n}^{3}; u_{0} \in] 0, 1 [

. s h o w t h a t u_{n} \in] 0, 1 [

. s h o w t h a t u_{n} c o n v e r g e s t o 0

v_{n} = \frac{1}{u_{n + 1}^{2}} - \frac{1}{u_{n}^{2}}

. e x p r e s s v_{n} i n t e r m s o f u_{n}

. s h o w t h a t v_{n} c o n v e r g e s t o 2

f (x) = \frac{2 - x}{{(1 - x)}^{2}}

. s h o w t h a t f i s i n c r e a s i n g a n d d e d u c e t h a t

v_{n} i s d e c r e a s i n g

. s h o w t h a t v_{n} ⩾ 2

Answered by Berbere last updated on 15/Jun/24

t c h e k e x p r e s s i o n o f V_{n} = \dots ?

Commented by alcohol last updated on 16/Jun/24

c o r r e c t e d

p l e a s e j u s t s h o w t h a t v_{n} ⩾ 2

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