u-n-is-a-sequence-and-lim-n-u-n-l-let-v-n-1-2-n-k-0-n-C-n-k-u-k-prove-that-v-n-l-n-

Question Number 36922 by maxmathsup by imad last updated on 07/Jun/18

(u_{n}) i s a s e q u e n c e a n d {l i m}_{n \to + \infty} u_{n} = l l e t

v_{n} = \frac{1}{2^{n}} \sum_{k = 0}^{n} C_{n}^{k} u_{k} p r o v e t h a t v_{n} \to l (n \to + \infty)

Commented by math khazana by abdo last updated on 10/Jun/18

w e h a v e v_{n} = \frac{\sum_{k = 0}^{n} α_{k} u_{u k}}{\sum_{k = 0}^{n} α_{k}} \to l d u e t o s e z a r o t h e o r e m

a n d \sum_{k = 0}^{n} α_{k} = \sum_{k = 0}^{n} C_{n}^{k} = 2^{n} .