GATE CS 2015 Set 3 — Question 20
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Algorithms → Asymptotic Analysis → Asymptotic Notations
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Question
Consider the equality and the following choices for
I.
II.
III.
IV.
The equality above remains correct if is replaced by
I.
II.
III.
IV.
The equality above remains correct if is replaced by
Correct answer
(C) I or III or IV but not II
Solution
The sum of cubes of the first natural numbers is given by:This expression is of the order , so:
- It is (Statement I is correct).
- It is NOT (Statement II is incorrect).
- It is because for large (Statement III is correct).
- It is because for large (Statement IV is correct).
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