# Thread: Sequence...

1. ## Sequence...

Let $(a_n)^\infty_{n=1}$ converges to $a$.

Is the next sequence $b_n$ also converges?

$b_n=\frac{a_1^2+a_2^2+\dots +a_n^2}{n}$

Thanks!

2. Originally Posted by Also sprach Zarathustra
Let $(a_n)^\infty_{n=1}$ converges to $a$.
Is the next sequence $b_n$ also converges?
$b_n=\frac{a_1^2+a_2^2+\dots +a_n^2}{n}$
Do you know the idea of the sequence of means?
Because $\left(a_n\right)$ converges it is true that $\left(a_n^2\right)$ also converges.