$$\text { Show that } 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + \cdots + n ^ { 3 } \text { is } O \left( n ^ { 4 } \right)$$

Name: \[\text { Show that } 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + \cdots + n ^ { 3 } \text { is } O \left( n ^ { 4 } \right)\]
Brand: Quizplus
Rating: 4.8 (37 reviews)

Question

Quizplus · Accepted Answer

The Answer is We have

1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + \cdots + n ^ { 3 } \leq n ^ { 3 } + n ^ { 3 } + n ^ { 3 } + \cdots + n ^ { 3 } = n \cdot n ^ { 3 } = n ^ { 4 }

whenever

n

is a positive integer. It follows that

1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + \cdots + n ^ { 3 }

is

O \left( n ^ { 4 } \right)

, with witnesses

C = 1

and

k = 1

.

Show that 13+23+33+⋯+n3 is O(n4)\text { Show that } 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + \cdots + n ^ { 3 } \text { is } O \left( n ^ { 4 } \right) Show that 13+23+33+⋯+n3 is O(n4)

$\text { Show that } 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } + \cdots + n ^ { 3 } \text { is } O \left( n ^ { 4 } \right)$