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