If $\displaystyle a_n$ converges to 0, does $\displaystyle \frac{a_n}{2}$ converge to 0?

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- Apr 24th 2010, 11:22 AMsfspitfire23converge
If $\displaystyle a_n$ converges to 0, does $\displaystyle \frac{a_n}{2}$ converge to 0?

- Apr 24th 2010, 11:31 AMKrizalid
yes.

- Apr 24th 2010, 11:34 AMsfspitfire23
thx

- Apr 24th 2010, 12:02 PMharish21
**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 $\displaystyle \frac{a}{b}$.

$\displaystyle lim (n\rightarrow \infty) [\frac{a_n}{b_n}] = lim (n\rightarrow \infty) [a_n \times \frac{1}{b_n}]= a \times \frac{1}{b} = \frac{a}{b}$