# How to prove that {1/2^n} is bounded series ?

Apr 13, 2017

$\left\{\frac{1}{2} ^ n\right\}$ is bounded since $0 < \frac{1}{2} ^ n \le q \frac{1}{2}$.

#### Explanation:

For all natural number $n$,

(a) $0 < {2}^{n} R i g h t a r r o w 0 < \frac{1}{2} ^ n$

(b) n geq 1 Rightarrow2^n geq 2^1 Rightarrow 1/2^n leq 1/2^1

So, $0 < \frac{1}{2} ^ n \le q \frac{1}{2}$ for all natural number $n$

Hence, $\left\{\frac{1}{2} ^ n\right\}$ is bounded.

I hope that this was clear.