#testbook

Question

Time complexity=$\sum_{i=1}^{n}[\log (\frac{n}{i})] is$

 

 

 

Comments

https://kconrad.math.uconn.edu/blurbs/analysis/stirling.pdf

the formula can be simplified to $\lg n^{n}/n!$ 

now we can write it as 

$n\lg n - \lg n!$

$\lg n!$ can be approximate to a certain value called stirlings formula.

in the link link you will find the formula, use it to put values and simplif to get answer

Answer 1

You need To know Some basic Property of log

1^st Property is   log(a/b)= Log(a)-log(b)

2^nd Pro property is  log(a)+log(b)+log© =log(a*b*c)

3^rd Property is   In summation(1 to i) of any Constant we can take Constant out side From Summation(1 to i)

Now you can solve easily