# Problem with summation, how did he find this result?

1. Oct 22, 2011

### Jncik

1. The problem statement, all variables and given/known data

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 [Broken]

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

Last edited by a moderator: May 5, 2017
2. Oct 22, 2011

### 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.

3. Oct 22, 2011

### LCKurtz

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.

Last edited by a moderator: May 5, 2017
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