Hi... can anyone help me with this ?

looks simple, i know! but i forgot the method =(

basically i want to expand

the sum of r between r = 1 upto n-1

to get

1/2n(n-1)

how would i do this?

thanks!

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- Mar 16th 2010, 04:13 PMmatlabnoobGeometric Progression
Hi... can anyone help me with this ?

looks simple, i know! but i forgot the method =(

basically i want to expand

the sum of r between r = 1 upto n-1

to get

1/2n(n-1)

how would i do this?

thanks! - Mar 16th 2010, 04:49 PMArchie Meade
- Mar 16th 2010, 05:13 PMmatlabnoob
thank you for your help!

i understood that. now im trying to do the same for ... r^2...

and im getting the same answer as for r

am i right to use the same method for r^2??

thanks again!=] - Mar 17th 2010, 02:55 AMHallsofIvy
Doing

**what**with r^2? You titled this "geometric progression" but the first example you gave was an arithmetic progression. What is it you are trying to do? - Mar 17th 2010, 05:08 AMArchie Meade
No, you cannot use the same method.

The previous one shows how to develop a formula for summing consecutive natural numbers.

If you want to sum consecutive squares, that's more involved.

You would need to understand the previous one quite well before attempting

to find a quick way to sum squares.

Here is a way to do it using "telescoping".

If you want to sum squares from r=1 to n-1, then you could use the following

Telescoping

all the way to

When these are summed, all terms except and 1 cancel.

Hence

2 summed n-1 times is 2(n-1)

Hence

If we sum all the way to n, this is more commonly known as the sum of squares