Problem with summation, how did he find this result?

[Jncik]

Homework Statement

Hi

I was trying to understand an algorithm analysis problem and I came to this point:

[PLAIN]http://img820.imageshack.us/img820/1834/unledytw.png

can someone explain me what he did there? Is there any other step between that should have been written in order for it to be more comprehensible?

thanks in advance

 

[Mr.Miyagi]

There may be a relevant identity, but in any case you can write out the first double summation and rearrange the terms in order to get the second equality.

(2/2 + 2/3 + ... 2/n) + (2/2 + 2/3 + ... 2/(n-1)) + ... + (2/2)
= (n-1)*2/2 + (n-2)*2/3 + ... + 1*2/n

All that remains is to convince yourself that this is actually what the second line reads.

 

[LCKurtz]

Homework Statement

Hi

I was trying to understand an algorithm analysis problem and I came to this point:

[PLAIN]http://img820.imageshack.us/img820/1834/unledytw.png

can someone explain me what he did there? Is there any other step between that should have been written in order for it to be more comprehensible?

thanks in advance

You are summing over a triangle in the k-i plane:

[URL]http://math.la.asu.edu/~kurtz/pix/doublesum.jpg[/URL]

It is just like reversing the order of integration in a double integral. You can read the limits from the picture.