00:01
Hello students, given that ith step requires i square operation.
00:07
So, the total number of operations total number of operations p of n for an input size of n is given by p of n equal to 1 square plus 2 square plus 3 square plus up to n square.
00:34
This is a sum of square and there exist a formula for the sum of the first n perfect square.
00:42
So, this is equal to n into n plus 1 into 2n plus 1 by 6.
00:52
Now, let's substitute this formula into the expression.
00:56
So, this is equal to tn.
00:59
Now, we expand and simplifying.
01:01
So, this is equal to 2n cube plus 3n square plus n divided by 6.
01:10
Now, let's find a constant c such that tn less equal to cn cube for all n greater than some value of n 0.
01:21
So, therefore tn equal to this.
01:23
So, this is equal to 1 by 6 into 2n cube plus 3n square plus n 2n cube plus 3n square plus n which is less equal to 1 by 6 into 2n cube plus 3n cube plus n cube.
01:48
Since n square must be less equal to n cube and n less equal to n cube for n greater than equal to 1...