If $\displaystyle a_n$ converges to 0, does $\displaystyle \frac{a_n}{2}$ converge to 0?
The quotient property of convergent sequences: If a sequence $\displaystyle a_n$ converges to a number a, and the sequence $\displaystyle b_n$ converges to a number b, with $\displaystyle b_n $ not equal to 0 for all indices n, and b is not equal to 0, then the sequence of quotients $\displaystyle \frac{a_n}{b_n}$ converges to the quotient $\displaystyle \frac{a}{b}$.
$\displaystyle lim (n\rightarrow \infty) [\frac{a_n}{b_n}] = lim (n\rightarrow \infty) [a_n \times \frac{1}{b_n}]= a \times \frac{1}{b} = \frac{a}{b}$