Find Time complexity

Question

Answer 1

1) 1^2+2^2+3^2+.......n^2=  n(n+1)(2n+1)/6

So it's O(n^3)

2) 1+1/2+1/3+......1/n =log no 

So it's O (log n) 

3)1/2+1/4+1/8+.... 1/2^n 

4) x+x^2+x^3+.......x^x

​Here dominating term is x^x so it O( x^x) 

5) x+2x+...... To infinity 

Here O(infinity) 

6)  for n! it's order of O(n^n) 

Log n! = O of Log n^n and ( log n!)! = O((log n^n) ^ log n^n) 

I'm not sure about 3 and 6

Comments

Can you please explain Q.2 ?
@Pranay Datta 1

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https://gateoverflow.in/13587/solve-the-recurrence

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My mistake in Q2)

Thank u sir I got it

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3rd is O(1)

Answer 2

3-i think .5^n

4-x^n

 

Apply gp..