Recent content by alyks

Organic Chemistry II - A Lab - A Physics II - A Calc III - A Humanities class - A Something called "Culture and Health" - A

Homework Statement Prove the following when p is a positive integer: b^p - a^p = (b-a)(b^{p-1}+b^{p-2}a+b^{p-3}a^2+...+ba^{p-2}+a^{p-1}) Hint: Use the telescoping property for sums. Homework Equations None The Attempt at a Solution I tried reducing it to, (b-a)\sum_{k=1}^p...

I'm mostly through Spivak as my first exposure to calculus. If your algebra is solid, and you're very thorough in studying the book (laboring over every detail in the chapters), then you'll get a better calculus education than a more watered down approach. You can compensate for less...

Yes. I would first assume that x is an element of the left hand side and do a prove by cases, then do the same assuming x is an element of the right hand side.

I highly recommend Velleman's How to Prove It: A Structured Approach. I went through the book knowing nothing about proofing beforehand and doing so helped a lot when making the transition to proofing.

Oh wow, it does save a lot of confusion with the min, I was thinking about it wrong.

Hi, I've been studying from Spivak's Calculus. Normally when I have trouble I can just search, but this time I can't find anything (you can tell how extensive this forum is in that I've been registered here for a while and this is my first post). On page 89, the book gives proof of the...