Bir dizinin bir

Question

İzin Vermek {$a_n$} b ve N sayıları olacak şekilde bir dizi olacak şekilde $\ge$ N, $a_n$= b. Kanıtla {$a_n$} b'ye yakınsar.

I am not sure how to go about this question. The information we are given does look very similar to the definition of convergence, but I'm not quite sure how to prove this given the information available.

Any help would be appreciated, I will try to answer comments as soon as possible.

Answer 1

It is given that there exists an $N$ such that for any $n\ge N$ we have $a_n=b$ so for any $\epsilon>0$

$|b - b| = 0 <\epsilon$ which means that $a_n\to b$ as $n\to\infty$