Aymptotic notation

Question

Consider $\sum_{i=0}^n{}$ i3 =x.what can be X

1.theta(n4)

2.theta(n5)

3.O(n5)

4.$\Omega$(n3)

Comments

except 2 all seems to be correct to me.

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correct $2$ is false rest are true

Answer 1

0³ + 1³ + 2³ + . . .n³ = 1/4(n²(n+1)²) = 1/4 * n⁴ + some other terms

Asymptotically <= n⁴, hence O(n⁵) is true. Therefore option 1 and option 4 is also true beside option 3

Comments

but 4 is the degree so it should be less that n⁴

O(n⁴) indicates worst case , which means it the worst possible so then how O(n⁵) is possible

where am i going wrong

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I may be wrong as well.
What my understanding is, <= n⁵ is valid as well, as it will cover n⁴

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but suppose for quick sort what do we say

we say worst case is O(n²) which means there is no way it can above that right?

okok i got it

theta value is n⁴ not  O(n⁴)

Answer 2

All Options are correct except Option 2.