Unravel the Code! 2025 Algorithms Analysis Test – Ace It Like a Pro!

Question: 1 / 400

Is 2^(n+1) = O(2^n)?

True

False

To determine whether 2^(n+1) is O(2^n), we need to analyze the relationship between these two functions. The Big O notation is used to describe the upper bound of a function's growth rate.

The expression 2^(n+1) can be rewritten as 2^n * 2. When we consider the definition of Big O notation, we say that a function f(n) is O(g(n)) if there exist constants C and n0 such that for all n ≥ n0, the following holds:

f(n) ≤ C * g(n).

In this case, we would need to show:

2^(n+1) ≤ C * 2^n for sufficiently large n.

Rearranging the inequality yields:

2^n * 2 ≤ C * 2^n.

Dividing both sides by 2^n (assuming 2^n > 0 for large n) results in:

2 ≤ C.

This means that for any constant C greater than or equal to 2, the inequality holds true.

Thus, since we can choose C = 2 (or any larger value), we can conclude that 2^(n+1) is indeed O

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Indeterminate

Cannot be determined

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