Finding a formula for the following summation

[rxh140630]

Homework Statement

$n^2 + (n-2)^2 + (n-4)^2...$
where n is a natural number

Relevant Equations

none

ive used google

https://www.google.com/search?q=n^2...i61j69i60l2.4719j0j7&sourceid=chrome&ie=UTF-8

and I was surprised that there was no relevant formula found

How do I get/even begin to get the formula for such a sum? I know it must be at least n^2 but that's it..

 

[PeroK]

When are you going to terminate the sum?

 

[rxh140630]

When are you going to terminate the sum?

The sum terminating depends on n. I don't know how to come up with a general formula for all n though

 

[PeroK]

The sum terminating depends on n. I don't know how to come up with a general formula for all n though

You mean you stop before the terms get negative.

 

[rxh140630]

You mean you stop before the terms get negative.

Yes. I'm assuming you're hinting at induction but the trouble is I can't think of a proper hypothesis in the first place..

 

[PeroK]

Yes. I'm assuming you're hinting at induction but the trouble is I can't think of a proper hypothesis in the first place..

I haven't thought about it. From what you say, you want either:
$$1 + 9 + 25 + \dots + (2k+1)^2$$
Or
$$4 + 16 + \dots + (2k)^2$$

 

[Mark44]

You mean you stop before the terms get negative.

None of the terms will be negative, since they are squared quantities. I'm sure you meant something more like stopping before n - 2k gets negative.