Simplifying ∑(i=1 to log(n)) 1/(log(n) - i)

[RoboNerd]

Hello everyone!

I have this expression which I have to simplify:
∑_i=1^log(n) 1^{(log(n) - i)}

And my book apparently simplifies it to being log(n).
I am struggling to figure out why this is the case. Could anyone help?

Thanks!

 

[fresh_42]

What is $e_i=1^{\text{ insert any integer }}$ and what is $\sum_{i=1}^{n} a_i$ if you write it out with dots? And finally set $a_i=e_i$.

 

[andrewkirk]

Firstly, how many terms are there in the sum - ie how many things are being added together?

Secondly, what is the value of each term? What do you get when you raise 1 to the power of any other real number?

EDIT: Uh oh - Jinxed again!

 

[RoboNerd]

Ohh, I see thanks!

We add 1 log(n) times over and over again!

Thanks for the help everyone!