VirtualGate

Question

Why can't be 3 is correct??

Comments

rewrite 3 as

2^n * 2^n * 2 = O(2^n)

now check yourself

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Ok got it Thank you.

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Given $2^{2n+1} = O(2^{n})$, both functions are exponential but $2^{2n+1}$ grows faster than $2^{n}$ for large values of n.

We can check by substituting any large value of n or one more way to see we can remove the Common function from both the sides, $2^{n}$ is common on both the sides, removing it we get $2^{n+1}$ in LHS and 1 (constant) in RHS. 

Clearly $2^{n+1}$ is greater than constant

So it is FALSE 

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O(2²ⁿ) not equal to O(2ⁿ), you may look at this question this way too!