Dear members,

I received the following proof from Mark Hurd. Using the new SUM
shortcut, he proved that

x + x^2 + x^3 + ... + x^k = x*((x^k-1)/(x-1)) for x>1

Well done, Mark!

Download by clicking on:

http://www.dcproof.com/SumPowers.proof (130K)

Dan

PS: I will soon be releasing a new version of DC Proof with improved
graphics in the user documentation.


Mark wrote:

> Dan
>
> Here's a proof that Sum(i,1,k):x^i=x*(x^k-1)/(x-1)
>
> It was developed during beta testing of the release below.
>
> Some of the premises (and lemmas) are not used, I got sidetracked
> in a
> couple of places, and I'd approach it slightly differently if I
> started
> again.
>
> Regards,
> Mark Hurd, B.Sc.(Ma.) (Hons.)