- #1
r4nd0m
- 96
- 1
I am really stuck with this excercise:
Let [tex]a_n and b_n[/tex] be two sequences, where [tex]b_n = \frac{a_1 + a_2 + ... + a_n}{n}[/tex] and [tex]lim_(n \rightarrow \infinity) a_n = a[/tex] prove that [tex]lim_(n \rightarrow \infinity) b_n = a[/tex].
I tried to use the definition - [tex]\mid b_n - a \mid < \frac{\mid a_1 - a \mid + \mid a_2 -a \mid + ... + \mid a_n - a \mid}{n}[/tex], but i don't know how to proceed. Any ideas?
Let [tex]a_n and b_n[/tex] be two sequences, where [tex]b_n = \frac{a_1 + a_2 + ... + a_n}{n}[/tex] and [tex]lim_(n \rightarrow \infinity) a_n = a[/tex] prove that [tex]lim_(n \rightarrow \infinity) b_n = a[/tex].
I tried to use the definition - [tex]\mid b_n - a \mid < \frac{\mid a_1 - a \mid + \mid a_2 -a \mid + ... + \mid a_n - a \mid}{n}[/tex], but i don't know how to proceed. Any ideas?