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Working on a Computer Science Fundamentals assignment and came across this. I see that I am supposed to find a $C$ for something... but that is about all i know. Can anyone break this down for me?

Thanks in advance.

Siong Thye Goh
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djjeane
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2 Answers2

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Hint:

  • Try to compute $\lim_{n \to \infty} \frac{3^{2n}}{3^n}$.
  • Conclude if $\frac{3^{2n}}{3^n}$ is bounded by a constant.
Siong Thye Goh
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$3^{2n}=\mathcal O(3^n)$ as $n\to \infty \iff \exists M: 3^{2n}\le M\cdot 3^n$ as $n\to \infty $.

$\frac{3^{2n}}{3^n}=3^n\to \infty$ as $n\to \infty$.

$\therefore \not \exists M: 3^{2n}\le M\cdot 3^n$ as $n\to \infty $.

So no.