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

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Answer 1 · 2017-04-13T02:08:55

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

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.

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