Hi

This time I'd like to know how to show this:

Attachment 28706

Thanks for the help.(Hi)

I edit: This is my first attempt of proof...but I'm not too happy with it...it seems to work, but it's too vague...

Attachment 28708

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- June 30th 2013, 05:38 PMLeviathantheesperProduct of these sums is a sum of the same form...
Hi

This time I'd like to know how to show this:

Attachment 28706

Thanks for the help.(Hi)

I edit: This is my first attempt of proof...but I'm not too happy with it...it seems to work, but it's too vague...

Attachment 28708 - June 30th 2013, 06:38 PMchiroRe: Product of these sums is a sum of the same form...
Hey Leviathantheesper.

Is y a constant for all k or does it change for a specific k? - July 1st 2013, 07:25 AMHallsofIvyRe: Product of these sums is a sum of the same form...
The way you have written it, with y constant, it is not true. (Hence chiro's question.) Rather you need something like

That is, you need that "y" different for each power of x and, obviously, if you are multiplying two nth degree polynomials together, you do NOT get an nthe degree polynomial, you get a 2n degree polynomial:

(a+ bx)(c+ dx)= ac+ (ad+ bc)x+ (bd)x^2. - July 1st 2013, 10:56 AMLeviathantheesperRe: Product of these sums is a sum of the same form...
Yes, y is not a constant, that was my mistake.

And...I know i don't get a nth degree polynomial... I edited some time ago to change the picture and replace the n with infinite (I replaced it yesterday)...

And the only thing I have to prove is that the result is a sum of the same form.

This, correcting the with

http://mathhelpforum.com/attachments...e-form-asd.png - July 1st 2013, 11:45 AMHallsofIvyRe: Product of these sums is a sum of the same form...
Again, that certainly is NOT true! Unless you mean, as both chiro and I said before, you mean .

And, in that case, it is pretty close to trivial. The product of any two terms, times must be of the form so the only thing you**can**have are "numbers times non-negative powers of x" and that is**all**the term "**means**! - July 1st 2013, 11:52 AMLeviathantheesperRe: Product of these sums is a sum of the same form...