How to sum sequence of floors numbers?

NumOne · 2012-02-01 12:02:07

How can I sum the following sequence:

∑ k∈{⌊n∕2⌋n-1}k = ⌊n∕2⌋ + ⌊n+1∕2⌋ + ⌊n+2∕2⌋ + ...... + (n-1)

(In another form)

n-1
∑ k = ⌊n∕2⌋ + ⌊n+1∕2⌋ + ⌊n+2∕2⌋ + ...... + (n-1)
⌊n∕2⌋

What I think is discard the floor and sum what inside each floor !! This is just a guess.

Give me any hint or general formula that helps me to sum them

Thanks

bobbym · 2012-02-01 15:15:47

Hi NumOne;

I am not following your notation. Nearest I can guess is that it looks like this:

Is this close?

NumOne · 2012-02-01 15:56:41

Actually, I got what I want but I got another problem which is :

I want to simplify the following equation:

(because I am not allowed to post any link, I'll give you the link without http)
img201.imageshack.us/img201/9801/codecogseqnh.gif

to be this equation:

(3/8)n^2

or

(3/8)n^2 - (.................) << anything else in the blank

I hope you get what I need

Thanks

bobbym · 2012-02-01 16:16:29

Hi;

Clean up the numerator:

So you have:

Multiply top and bottom by 1 / 2.

Which is one of the forms you requested.

NumOne · 2012-02-01 17:05:44

Thank you very much. That was very helpful.

Appreciate it.

bobbym · 2012-02-01 19:54:19

Hi NumOne;

Your welcome.

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