Question

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

Answer 1

`{1/2^n}` is bounded since `0<1/2^n leq1/2`.

Explanation:

For all natural number `n`,

(a) `0 < 2^n Rightarrow 0 < 1/2^n`

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

So, `0<1/2^n leq 1/2` for all natural number `n`

Hence, `{1/2^n}` is bounded.

I hope that this was clear.