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

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

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Answer 1 · 2017-04-13T02:08:55

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

Explanation:

For all natural number $n$ $n$ ,

(a) $0 < 2^{n} \Rightarrow 0 < \frac{1}{2^{n}}$ $0 < 2^n Rightarrow 0 < 1/2^n$

(b) $n \geq 1 \Rightarrow 2^{n} \geq 2^{1} \Rightarrow \frac{1}{2^{n}} \leq \frac{1}{2^{1}}$ $n geq 1 Rightarrow2^n geq 2^1 Rightarrow 1/2^n leq 1/2^1$

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

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

I hope that this was clear.

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

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