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**i, I'm stumped on a proof, one problem may be that either I don't know how to deal with exponents of this type, or my algebra went wrong somewhere. It's from the first chapter of Courant's book "What is mathematics" (p.18 q4)**

1. Homework Statement

1. Homework Statement

Prove by mathematical induction:

[itex](1 + q)(1 + q^2)(1 + q^4)[/itex] ... [itex](1 + q^{2^n})[/itex] (it doesn't come out clear, but q is raised to the power 2 and then 2 is raised to the power n) [itex]= \frac{1-q^{2^{n+1}}}{1-q}[/itex]

Again, this is meant to be that q is raised to the power 2, which is then raised to the power n+1. It's coming out strange and I'm not sure how to fix it, so my apologies (and any advice on how to make this look better would be welcome).

Mod note: In LaTeX, put exponents in braces ({ }), not parentheses. I fixed the above for you.

So i let n=k, then tried with n=k+1 and the algebra got really nasty. Usually when this happens, I've made a mistake. I ended up with this [itex]q^{2^{(k + 1)^2}}(q-1) - q + 1[/itex].

Mod note: I this this is what you're trying to say, above.

Please note, I again cannot get this equation to come out how it should and the parentheses are misleading; it should read q raised to the power 2, which is itself raised to the power k+1, which is itself raised to the power 2. This is as simple as I could make the LHS look, which of course, is not very simple at all. ANY help would be appreciated as I am completely stumped, and it's very possible I've gone in completely the wrong direction here. I've also read through the advice on this forum about Latex and I looked on the web and couldn't find any info on how to get what I wanted (as in, exponents with exponents themselves).

Thanks

Thanks

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