Hi there,

I am proving something, and I want to know how to rewrite a formula like this one: a^x - b^x, where you know that b<a.

Is there any way to write this differently? Maybe with sumformula, or an easy powerrule...anything?

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- Nov 13th 2009, 03:15 AMMaryBHow can you rewrite powers like this: a^x - b^x?
Hi there,

I am proving something, and I want to know how to rewrite a formula like this one: a^x - b^x, where you know that b<a.

Is there any way to write this differently? Maybe with sumformula, or an easy powerrule...anything? - Nov 13th 2009, 03:57 AMHallsofIvy
- Nov 13th 2009, 04:42 AMMaryB
Actually, that is a very useful rewriting you gave me there.

Does it have a name? Or is it deduced from another formula?

I think I can use it! - Nov 13th 2009, 08:45 AMMoo
Hello,

See here : http://www.mathhelpforum.com/math-he...484-k-b-k.html for a way to prove it :) - Nov 13th 2009, 09:26 AMMaryB
Brilliant thanks! Btw, I love your avatar.

Okay well, my assignment is getting near the solution, but not yet. So I now have $\displaystyle (a- b)(a^{x-1}+ a^{x-2}b+ a^{x-3}b^2+ \cdot\cdot\cdot+ a^2b^{x-3}+ ab^{x-2}+ b^{x-1})$ and found out that if a = a+1, then b = a. so...now I have $\displaystyle (a+1 -a)((a+1)^{x-1}+ (a+1)^{x-2}a+ (a+1)^{x-3}a^2+ \cdot\cdot\cdot+ (a+1)^2a^{x-3}+ (a+1)a^{x-2}+ a^{x-1})$

And yeah, okay. How can I rewrite this one? I don't think it's neccesary to give the whole rewriting, but a hint? (Or the whole rewriting is okay, I can stop myself from looking first and try it out myself). - Nov 14th 2009, 02:37 AMMaryB